It begins as the most ordinary of stories and ends with three women who are trapped in a small apartment in a country I can’t name. If they are found here, they will be in danger, but they have nowhere else to go. They are queer refugees from a Muslim country, which means that the world doesn’t have a place for them.

To piece together the story of Alisa, Sasha, and Elya (not their real names), I interviewed them by Skype and talked with four different people who witnessed various portions of their journey. The three women have been on the run from their native Chechnya for more than six months.

All three are between the ages of twenty and twenty-five. Alisa worked as a civil servant in Grozny, the capital of Chechnya. Sasha, who had recently graduated from college with a degree in economics, was working at a menswear shop and making a small fortune in commissions. Elya was studying computer science at the university in Grozny. Sasha and Alisa are a couple. All three belonged to a small, closed group of young Grozny lesbians, where, as it happens in lesbian communities the world over, half the women had slept together, half wanted to sleep together, and several had been through rancorous breakups. The women in this group had known one another for a couple of years.

Last winter, four young women from this small community were caught, in the basement of the local university, drinking and smoking weed. The police took them into custody. For women to be drinking and smoking in Chechnya was reason enough for their arrest and, likely, for the disgrace that would follow, but in their cases things were going to get even worse. From what their friends were able to piece together from rumors—someone had a relative in law enforcement, and Alisa worked in the government, so they heard things—the four women were taken to the unit that, as Elya put it, “deals with L.G.B.T.”

For the last year and a half, Chechnya has been conducting an anti-gay purge. Men have been kidnapped, tortured, and, in several cases, killed. Their stories have been told by journalists and human-rights activists. Much less is known about what happens to lesbians, in part because very few women leave the region. It is also possible that the direct violence of the purge has affected women less because they are less likely than men to act against familial and societal expectations, and therefore less likely to be caught breaking rules outside the home. And, yet, here were the four women, detained for misbehaving, and their friends assumed that their entire little group was now under threat. To make matters worse, Alisa’s former girlfriend was among those detained, and, because of the way things had ended between them, Alisa was sure that it wouldn’t be long before the woman gave Alisa’s name to the authorities.

Sasha, Elya, Alisa, and a fourth friend had huddled together. They considered running away, but their disappearance would bring shame upon their families, so they decided to stay. Then, from someone who is married to a law-enforcement officer, they heard that the four detained women were being raped. At around the same time, Alisa, through her government connections, learned that law enforcement had compiled a list of known or suspected lesbians. Meanwhile, Elya got word that the university dean wanted to see her. They felt cornered. They decided that, if they stayed and got arrested, that would bring shame to their families, too, so they may as well try to survive. One of them knew a Western human-rights activist who often worked in Chechnya. They asked this person for help getting out.

During the last year and a half, the Russian L.G.B.T. Network has extricated well over a hundred L.G.B.T. people from Chechnya and has helped most of them make their way out of Russia altogether. The vast majority of them have been men. It’s easier for a man: he can tell his family that he is going to leave the region to look for work, and this is no one’s decision but his own. A woman cannot make a move without her family’s permission. A friend of Elya’s was forcibly married off to an older man at the age of seventeen, in large part, apparently, because the family suspected that she was a lesbian. Early on in the Russian extrication efforts, a young woman whom the Network had helped leave Chechnya was found and taken back by her parents, only to turn up dead a few days later. In a later case, the family intervened just as a woman was about to leave the country. (In this instance, though, activists eventually succeeded in wrenching the woman away.)

On the morning that the young women were supposed to meet the driver who would take them out of Chechnya, the fourth woman told the others that her mother was stopping her. The remaining three got on the road. Each of the women wrote a letter to her family asking them not to look for her. Each carried one duffle bag, in which warm clothes took up most of the space: it was winter. Each also grabbed some family photographs, though most of the memories they carried with them were on thumb drives.

The driver, who was not Chechen, took them to a city outside of Chechnya, where they switched cars and kept going. After about two and a half days on the road, the three women were delivered to Russian activists who set them up in a safehouse. A few days later, the women found out that all of their families had filed missing-person reports.

They had a lawyer now, who went to Chechnya with affidavits showing that the women had left Chechnya of their own accord. The lawyer returned with bad news: the families were claiming that the women had been kidnapped and were demanding a full criminal investigation of their disappearance and, they said, their possible murder. The next time the lawyer travelled to Chechnya, he brought depositions in which the women said that they had left because they were lesbians. The lawyer went back and forth several times, delivering more and more evidence that the women were alive, well, and unwilling to be reunited with their families, but after three or four months of negotiations he concluded that the Chechen authorities would never drop their search. The only hope they had for being able to leave the country lay in finding a border crossing where agents either didn’t use the federal computerized database that would have flagged them or could be convinced to ignore it.

They decided to leave Russia via a virtually transparent land border; they carried invitations to an L.G.B.T. conference in a neighboring country. They hoped that border control at the land crossing was low-tech enough that they would not be flagged, and this part of the plan worked: they were allowed to cross the Russian border. Border-control officers of the neighboring country, however, raised an alarm when they saw that the women were from Chechnya and again when they saw their invitations from an L.G.B.T. organization. “They spent a long time inspecting our car,” Elya told me. “Then they took each of us into a separate room for questioning. They asked why we were travelling, and did our parents know. They talked to us like we were criminals. We kept saying that we are adults and we are on vacation. When they saw that we are lesbians, the border guard said they he didn’t have the right to let us in.” Not only did they have to turn around but their passports now bore “entry denied” stamps from the neighboring country, which meant that they could no longer try to use this route to get out of Russia.