Chimpanzee

Chimpanzees were a species of intelligent, but not sentient Earth primate. They were the closest biological relatives of the Human species.

When Doctor Phlox attempted to compare the DNA from a Xindi-Reptilian to a Xindi-Primate in 2153, he noted that the Primates' genetic profile was nearly identical, but not quite the same, as the Reptilians'. Despite this, he noted that their base pair sequence were significantly closer to each other than the base pair sequence of a Human and a chimpanzee. Phlox then agreed with Jonathan Archer that a closer analogy between the Primate and Reptilian might be a Human and a Neanderthal. 

In the daring plan to steal the USS Enterprise (NCC-1701) to rescue Spock from the Genesis Planet, Scotty automated the ship in such a way that "a chimpanzee and two trainees could run her." Upon hearing this description, Kirk thanked Scotty and noted that he would not "try not to take that personally." 

Background
According to the non-canon resource, Star Trek Spaceflight Chronology, in 2055 the Warp Drive Program resulted in the first vessel to exceed speed of light. A chimpanzee named Rosy that went along for the ride was safe and sound. This information has been contradicted by the later which showed Human test pilots Zefram Cochrane, William T. Riker and Geordi La Forge making that flight in 2063. However, the earlier flight may have been a previous unmanned experimental flight.