San Francisco came a big step closer to ending chronic homelessness for veterans Wednesday with the opening of a 70-unit supportive housing complex for people who have served in the military.

The complex is in the refurbished Auburn Hotel on Minna Street, near Sixth Street, and it brings to 300 the number of residential rooms or apartments opened in the past year in San Francisco for homeless veterans.

Filling these rooms means there are now fewer than 150 chronically homeless vets — meaning the most troubled, on the streets for at least a year — left living outside in San Francisco, according to Jeff Kositsky, head of the city Department of Homelessness and Supportive Housing.

Kositsky said the city hopes to all but eliminate chronic homelessness among veterans in 2018. In addition to getting the remaining chronically homeless vets off the streets, that will involve finding shelter for the estimated 17 additional veterans who fall into that category each month in the city.

Officials try to deal with the problem by opening residential buildings like the Auburn, handing out rent vouchers, and giving people bus tickets home if there are people waiting for them there.

“It’s been a challenge, but we’re still committed to getting there,” Kositsky said. He noted that in 2014, there were 350 chronically homeless veterans in San Francisco, and since then more than 900 have been housed.

Acting Mayor London Breed said at the Auburn that “we are well on our way” to ending chronic homelessness among veterans. She called the new complex “the least we can do for people who put their lives on the line time and time again.”

The Auburn is being leased by the city and managed by the nonprofit Delivering Innovation in Supportive Housing. Episcopal Community Services, another nonprofit, will provide counseling services on-site — a key component of the “supportive” part of supportive housing.

Kevin Fagan is a San Francisco Chronicle staff writer. Email: kfagan@sfchronicle.com Twitter: @KevinChron