About 2,400 unaccompanied minors are being held in shelters nationwide and most were detained at the U.S.-Mexico border and placed in the custody of the Office of Refugee Resettlement.

The Chicago shelter is operated by the nonprofit group Heartland Alliance, which also runs two other dormitory-style shelters for unaccompanied immigrant youth in Chicago. The children living at the shelters range from infants to teenagers.

The Administration for Children and Families said in a statement to ABC News on Thursday that a total of 39 unaccompanied immigrant children in its custody across the nation have tested positive and placed in medical isolation, indicating that the largest coronavirus outbreak in its system is at the Chicago shelter.

Positive cases have also turned up at two shelters in Texas and 69 staff members affiliated with the Office of Refugee Resettlement have self-reported testing positive for COVID-19, according to the statement

However, the agency did not address what it is doing to reunite the children with family in the United States. But officials said that "out of an abundance of caution," it has stopped placing unaccompanied children in virus hotspots such as California, New York and Washington.

"The situation remains extremely fluid and can change rapidly. We are providing the latest information while working diligently to combat random speculation and rumors," according to the statement.

In a statement to ABC News on Thursday, Heartland Alliance said it had tested all the children in its care and that the positive coronavirus cases are contained to the one shelter in the Bronzeville neighborhood. The agency said that 76% of the 37 children to test positive were "completely asymptomatic at the time of testing."

"Heartland Alliance has aggressively tracked down and secured tests for our children and our staff -- knowing full well that children are often asymptomatic and can spread the virus even more easily than others," the statement reads. "And we are committed to ensuring access to testing for our staff because it's imperative for their health and well-being, and that of their families and the larger community."

The agency described the prognosis for the children as being "very good, and they are doing well."

Heartland Alliance declined to comment on whether any of the agency's 500 staff members have tested positive.

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"We have been encouraging our staff to access their medical providers for testing and, as we all know, it is hard to gain access to tests," according to the agency's statement. "We have fought hard to obtain test kits for our staff, and we are beginning to roll out this voluntary testing process, in coordination with their health provider, and we are prepared to address the confirmed cases."

The agency said it has been closely following local, state and federal safety guidelines, including taking daily temperatures of staff and clients, frequent hand-washing and social distancing.

"When staff are sick with anything, they are sent home. And when anyone tests positive for COVID-19, we communicate with all with whom they have been in contact, and they too are put on quarantine," according to the agency's statement.

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Ashley Hueber of the National Immigrant Justice Center, which is affiliated with Heartland Alliance, said social distancing in such dormitory-type facilities is difficult.

"At the end of the day they are group settings. When you have anybody who is living in a group setting right now, it is nearly impossible to practice any kind of social distancing," Hueber told WLS-TV.

Chicago has been especially hard-hit by the virus also known as COVID-19. As of Wednesday afternoon, there were 386 deaths linked by the virus in Chicago and more than 10,000 positive cases, according to data released by the city.