These include the panting sounds made by chimps and dogs when they play and chirping sounds observed in rats.
This suggests that the capacity for laughter may be a very ancient emotional response that predates the evolution of humankind, says Panksepp.
Research suggests the capacity for human laughter preceded the capacity for speech.
(old article, I know)
And here's a video of rats giggling when tickled.
Some of you have rats, I believe, do ya'll's rats giggle like that?