The problem, Turbo, is that animals lack the rationality to overcome instinct. A dog's instinct has been purpose-bred for thousands of years, to please and obey its master. That's merely a modification of its original pack mentality. The squirrel, who is a link lower on the food chain (and has a brain the size of a pecan), doesn't know that the carnivorous dog has been bred to not eat it. Very long exposure is required for something that humans would interpret as "trust" to develop. "Trust" is a human concept, though. I'm no biologist or animal behaviourist, but my thought is that an animal's "trust" response is based solely upon an experiential lack of threats under certain circumstances.
That is assuming that the animals meet as adults or adolescents. Mutually hostile species, if raised together from birth, adopt the more basic instinct of imprinting upon each other as siblings. (I wouldn't expect it to work for a snake and a mongoose, but it seems to be pretty effective for all-mammal systems. I've seen rats being treated as kittens by cats. That was really cool, because those are my two favourite animals.)
By the bye, I just noticed that I've been referencing squirrels although the OP is about a chipmunk. That's a bit embarrassing, but it doesn't alter the things that I've said since they apply to any small fur-bearing animals.