Place the chicken breasts flat in the bottom of the slow cooker basin.
Whisk the brown sugar, soy sauce, rice vinegar, minced garlic, ginger, and reserved pineapple juice in a bowl. Pour over the chicken.
Cook on low for 4 to 5 hours until the chicken is tender and fully cooked.
Remove the chicken to a cutting board and shred it with two forks.
Pour the hot cooking liquid from the slow cooker into a saucepan over medium heat. Whisk the cornstarch and cold water together, then stir into the boiling liquid.
Simmer for 3 minutes until thick. Add the shredded chicken and reserved pineapple chunks to the pan, toss to coat, and serve.