Season the uncooked chicken breasts with ½ teaspoon of sea salt. (Time-saving option: Use pre-cooked roasted chicken breasts. If you are using this option, skip to step 3.)
In a skillet, warm the coconut oil to medium. Add the uncooked chicken breasts, and cook on each side until done through, approximately 12 minutes total depending on thickness. When done, use a fork to shred into chunks. (Alternately, you can also cook the chicken breasts in your Instant Pot using the "SAUTE" function.)
Add the chicken and remaining ingredients to an Instant Pot, beginning with 1/3 cup of balsamic vinegar, and placing the thyme sprigs on top.
Set to manual for 15 minutes; quick release the pressure at the end.
Place about 1/3 cup of spinach into separate serving bowls, then ladle the soup over the spinach just before serving.