There are primates that are more monogamous than humans. The cotton topped tamarin, for one.

he Cotton-top Tamarins have a monogamous breeding system and live in groups ranging from 1-19 individuals. However, the most common group sizes are from 3-9 individuals. These groups consist of a dominant mated pair, their young of the year, and a few subordinate or young animals of both sexes. These subordinate members tend to form small groups and migrate in and out of the home range of the main group. ....Males put forth more effort in caring for young than the females. The father assists at birth and carries the young all of the time exept when the mother is feeding.