Tsambido Hosea Abana, a community leader from the Chibok village, confirmed to CBS News that one of the girls, Amina Ali Darsha Nkeki, had been found in the Kulakaisa area on the edge of the Sambisa Forest.
She said a Chibok vigilante group on patrol Tuesday found Nkeki with a baby. She told them the other girls were still in the forest, which is a known hideout for the Boko Haram extremists.
Her uncle told the Associated Press that Nkeki was found traumatized, but otherwise fine.
The young woman told her mother that some of the Chibok girls have died in captivity and the others still are held by Boko Haram, according to family's doctor, Idriss Danladi, who spoke to The Associated Press after a conversation with the mother.
Yakubu Nkeki said his niece was found wandering in the forest. He said the 19-year-old -- she was 17 when she was abducted -- was brought to Chibok Tuesday night for her identity to be verified and reunited with her mother. Her father died while she was held captive, he said.
The Nigerian army released a statement, confirming that one of the Chibok girls had been found alive, but identifying her as Falmata Mbalala. The discrepancy in the girl's identity could not immediately be clarified.
Either way, she is the first of the girls to be found alive since the abduction on April 14, 2014 of 276 girls and young women from a boarding school in Chibok. Dozens managed to escape within hours, but 219 remained held by Boko Haram.
The mass-abduction prompted an international outcry against Boko Haram, which has since pledged allegiance to the Islamic State of Iraq and Syria (ISIS), sparking an outpouring of support on social media under the Twitter hashtag #BringBackOurGirls.
Many of the girls have likely been forced into sexual slavery by Boko Haram militants, sold as slaves, or brainwashed into becoming footsoldiers or suicide bombers for the group.
Early this year, video was broadcast giving the first indication that at least some of the girls were still alive.
CNN showed the video, believed to have been made in December, of girls wearing the Islamic hijab covering and of one mother reaching out to a computer screen as she recognized her daughter.
Nigeria's military tried to claim her rescue.
"This is to confirm that one of the abducted Chibok school girls ... was among the rescued persons by our troops," said a one-line statement from army spokesman Col. Sani Kukasheka Usman.
Hunters took the 19-year-old Nkeki - she was 17 when abducted - to her home village of Mbalala, near Chibok, on Tuesday and she reunited with her mother, Danladi said.
Her father died while she was held captive, said her uncle Yakubu Nkeki. Mother, daughter and baby have been taken to a military camp in the town of Damboa.
The girl's mother tried to commit suicide some months after her daughter was seized, said Danladi, who is from Chibok and has treated several of the parents.
He said the mother "suffered a huge traumatic disorder ... I had to convince her that she just has to stay alive if she really wants her daughter returned home safe and sound."
At least 16 of the girls' parents have died since the kidnapping, he said. Others have ailments they blame on their ongoing trauma.
"I suffered a stroke on Friday, that's why you don't recognize my voice," said the Rev. Enoch Mark, whose two daughters are among the missing girls.
He said the escape of the first Chibok girl brings renewed hope. "I believe that, by the grace of God, our daughters, some of them, will be found if they are still alive."
Other Chibok girls may have been rescued by soldiers hunting down Boko Haram in the remote northeastern Sambisa Forest on Tuesday night, said Chibok community leader Pogu Bitrus. He said he is working with officials to establish their identities.