The congregation has already performed at least one such ceremony said a spokesperson for Out North in the wake of last Thursday's decision by the United Church of Canada to officially approve homosexual marriages.
"It's already happened here," said Zoe Raemer, a spokesperson for the gay and lesbian advocacy group.
Raemer said Thursday's decision by the United Church of Canada to bless same sex unions is a victory for homosexual couples.
"It's very uplifting," she said. "The United Church is at the forefront of recognizing the dignity of gays and lesbians."
Some Canadian congregations of the United Church's have been performing same sex-unions since 1988, but the issue is still a delicate one for the head of Yellowknife's congregation.
Rev. Elizabeth Richards refused to confirm whether or not she had blessed a same sex-union.
"I'm not going to say," she said.
But Richards did say she would perform a ceremony if asked.
She also said the church had a responsibility to recognize the rights of homosexuals.
"We need to support gay and lesbian rights as a way of moving forward."
Same-sex couples still can't obtain a legal marriage licence in the NWT.
Under the current law, gays and lesbians can apply to be common partners but they first need to provide proof that they have been together for at least a year. Common-law couples also don't enjoy the same legal benefits as married couples.
"It definitely isn't the same," said Raemer.
Raemer is encouraged by recent appellate court decisions in the Quebec, Ontario and British Columbia that allowed same-sex couples to marry and federal legislation that would re-define the legal meaning of the word 'marriage' to include gay and lesbian couples.
"I think it's just a matter of time before gays and lesbians can legally marry in the NWT," she said.