The pileated gibbon was born several weeks prematurely, and there were fears that it would not survive.
The zoo began the breeding programme in 2001 and staff are "cautiously optimistic" they have achieved their first success with the rare primate.
Pileated gibbons are classed as endangered by the International Union for the Conservation of Nature.
More on the pileated gibbon, and other Devon and Cornwall news
The baby gibbon's parents are both nine years old, with its mother Shukdi born at Zoo d'Anson in France.
Curator of Mammals Neil Bemment said: "This is Paignton Zoo's first surviving pileated gibbon baby - I'm really pleased.
"As we have been trying to breed this species for 15 years, but alas our previous female was not a good mother."
A rare type of gibbon has been born at Paignton Zoo - after 15 years of trying.