It's the Chi side that is known for having running eyes. I would double check with your vet to make sure it isn't allergies/eye issues.
Otherwise, there are special solutions for tear staining that you can get at the pet store, if your Jack Chi is prone to that. When your dog gets a red eye, you can get saline solution (or boil water, let it cool, throw some salt and cotton balls in) - soak a cotton ball in it and squeeze it over your Jack's eye- and that should help.