I have a small container garden. Is it possible that squirrels or chipmunks are taking bits out of my unripe tomatoes? Are there any good remedies to prevent this?

Sure, place the containers on a high table where they can't climb up and help themselves to your stuff. Squirrels will eat just about anything that isn't nailed down that they can reach. Chipmunks are ground dwellers and don't climb much. It's hard to foil squirrels though.