Place the chicken breasts flat on the bottom of the slow cooker.
Whisk the soy sauce, brown sugar, rice vinegar, minced garlic, grated ginger, and half of the reserved pineapple juice in a bowl. Pour over the meat, then top with the pineapple chunks.
Cook covered on the low setting for 4 hours until the meat is cooked through and tender.
Remove the cooked poultry and shred it with two forks. Turn the appliance to high.
Mix the cornstarch and cold water to make a slurry. Stir it into the slow cooker juices, then add the shredded meat and chopped bell peppers back into the pot. Let cook uncovered for 10 to 15 minutes until the sauce thickens and the peppers are tender-crisp.
