Place 3 chicken breasts in the base of the slow cooker.
In small bowl, whisk together the tomato paste plus 2 cans worth of water, the cider vinegar, mustard, and brown sugar. Add a little salt and pepper is you wish. Add the chopped onion and crushed garlic to the sauce.
Pour sauce over chicken breasts. Set slow cooker to high and cook for 4-6 hours.
When chicken is finished in the slow cooker, scoop it out into a bowl and using 2 forks, "pull it" apart. Once "pulled"...scoop some sauce from the slow cooker and add until reaches your desired saucy-ness.
Slice bread. Place pulled chicken with sauce onto bread.
Serve Pulled Chicken Sandwiches with Side Salad.