Electric Pressure Cooker - Add the balsamic vinegar, honey, chicken broth and Dijon to the Instant Pot and whisk until well combined. Add the onion, garlic, thyme and chicken. Cook thawed chicken on high pressure for 12 minutes. (Cook frozen chicken on high pressure for 20 minutes.) Turn the pressure valve to “Vent” to release all of the pressure.
Remove the chicken breasts from the pot and place on a plate or cutting board. Shred the chicken using two forks.
Remove ⅔ cup of liquid from the pot. (Reserve the liquid for cooking rice.) Return the shredded chicken to pot and stir until well combined.
Crock Pot - Add the chicken breasts to a sprayed or lined Crock Pot. In a small bowl, whisk together the balsamic, honey and dijon. Top the chicken with the mixture along with the chicken broth, onion, garlic and thyme. Add an additional ½ c. chicken broth.
Cook on low for 4-5 hours. With 30 minutes of cooking time left, shred the chicken using two forks.
(If using frozen chicken in the Crock Pot, cook on low for 5-6 hours.)