The crash happened about 7:15 a.m. on Grand Avenue at the 71 Freeway overpass, according to a tweet from the city of Chino Hills' official Twitter account.
Whether the driver of the truck was injured was not immediately clear.
Firefighters and Inland Valley Humane Society officials responded to the scene, where chickens who remained in the cages were being removed individually.
The 71 Freeway's southbound off-ramp and Grand Avenue's eastbound lanes were closed at the scene as the investigation and cleanup operation continued.