Trim any excess fat and skin from the chicken thighs. Dry with paper towels and season on both sides with salt and pepper.
Press the "Saute" button on the Instant Pot. Press "Adjust" and select "More" setting. Once the display says "Hot", add the olive oil and allow to heat.
Once the oil is hot add the chicken skin-side down. Saute without moving until golden in color, 7 minutes. Flip and cook 2 minutes. Transfer to a clean plate.
Add onions and tomatoes, saute until tender, 3 minutes. Add garlic and saute for 30 seconds.
Add chicken broth, balsamic vinegar, ½ teaspoon salt and thyme, stir to combine.
Add chicken to the pot. Place lid on Instant Pot and turn to lock. Make sure the steam release handle is positioned to "sealing". Press the "Keep Warm/ Cancel" button.
Select the "manual" setting on "high pressure". Use the "- or +" button to adjust the time to 10 minutes.
It will take about 10 minutes for the pot to build steam and pressurize. You may see some traces of steam exit from the float valve as it is pressurizing.
Once the display indicates "On" and begins the countdown at "10", and beeps when the cycle is complete.
Cover your hand with an oven mitt or towel to carefully quick-release the pressure from the pot, sliding the steam release handle to the "Venting" position to release all of the steam until the float valve drops down.
Carefully open the lid. Press the "Keep Warm/ Cancel" button.
Transfer chicken skin-side up to a foil-lined sheet tray. Broil on high about 12-inches from the top of the oven to crisp the skin, about 3 to 5 minutes.
Meanwhile, press "saute" on the "more" setting. Simmer and stir until sauce is reduced and thickened, 8 to 9 minutes. The sauce should be reduced to about ¾ cup.
Taste and season with salt and pepper as desired. Serve sauce with chicken and garnish with parsley.
MAKE IT WHOLE30 AND PALEO: Use extra-virgin olive oil and sea salt.