In 1994, the Board of Immigration Appeals at U.S. Immigration declared asylum for a gay man from Cuba, essentially including sexual orientation as a new criterion.
"Since then, it's increasingly become an accepted reason for someone to seek asylum if they fear for their safety or freedom," said Victoria Neilson, legal director for Immigration Equality.
Unlike refugees, who are subject to quotas and apply for legal residency outside the United States, immigrants already in the U.S. can seek asylum "affirmatively."
But they have to meet strict criteria for a green card -- background checks and documentation of conditions in their native land.
The cost to hire good legal help can exceed $10,000, according to Neilson.
"Much of the work that an attorney does is taking raw and messy facts of someone's life and help shape them into coherent narrative that sort of meets up with legal standard for asylum," she said. "If someone doesn't represent them and they come from a different legal system or perhaps don't speak the language, it's extremely difficult to win."
If they fail, they are subject to immediate deportation.
"They go from being under the radar to into the headlights," Neilson said.
One of the hurdles, is that asylees must apply within one year of arriving in the United States.
"This is is something that has been disproportionately a problem for LGBT people," she said. "Many are not aware that sexual orientation or being transgender is a reason."
Immigration Equality makes sure applicants have a strong case and wins the majority of the cases it takes on, according to Neilson.
Countries with some of the worst records on LGBT rights are Saudia Arabia and Mauritania, both of which still have the death penalty for being gay.
In Jamaica, where criminal laws against homosexuality are not well-enforced, private citizens are responsible for most of the persecution.
"The police don't do anything to protect them from violence," Neilson said.
LGBT people have had their homes set on fire or been chased down the street by an angry mob and police routinely turn away victims seeking help, she said.
Last year, Immigration Equality won asylum for now 25-year-old Korey Chisholm of Guyana, an English-speaking South American country hostile to gays.
Chisholm was an AIDS activist who was infected with HIV after being brutally raped at 16. He entered the United States on a tourist visa last year and now lives in Brooklyn and works in a retail store. He is still involved in social justice organizations.
Chisholm was constantly taunted as a child for appearing effeminate and routinely denied access to public transportation because other passengers were not comfortable having a gay person ride with them.
Later, as a UNAIDS Fellow, he was treated well by colleagues, but shunned in any other setting.
"Getting transportation or just walking down the street for someone who is flamboyant or openly gay was very difficult," Chisholm said.
"Religious values play an important role in our country and the law is not as important as the Bible," he said. "If you are caught in the act, you face imprisonment and no one can help. You can't go to the police."
Chisholm has been robbed and he has gay friends who have been beaten.
Even being HIV positive, he was given no access to medicines until he arrived in the United States.
"I was very sick," he said. "But since coming here I am fine."
Neither Chisholm nor Oliver will be able to return to their native countries until they are citizens -- in about five years. But both say they are "excited" about their new lives.
Oliver, who lived at first in a shelter, is now temporarily living with friends. Finding work has been a challenge, but eventually, he hopes to go back to school to get a master's degree in public health.
"Hopefully, I will build on myself and when I am ready and able, I pray I can go back home and help," he said. "But now, I feel like one of the lucky few to live another day."