The Ape with chain was a character played by Hector Soucy, according to the credits of Conquest of the Planet of the Apes. No idea who this refers to. Despite suggestions, it's not the chimp beaten up in front of Caesar and Armando - that was Aldo, as played by David Chow.
The opening scene in the script depicts a frightened ape trying to escape the city and being shot by the security forces. While this scene didn't make it into the movie, it was filmed (and featured in the Marvel Comics adaptation), and it might just possibly be this character. Parts of that sequence were incorporated into Caesar's escape attempt later in the film, the guards and their uniforms changing slightly between shots. Until this mystery is solved, here's a picture of an ape... with a chain.