Add oil to the Instant Pot and set to 'Saute', until it reads 'Hot'. Meanwhile, sprinkle chicken thighs with salt and pepper, and place skin side down in a single layer in the bottom of the pot. You may have to work in batches. Cook, undisturbed for 8 to 10 minutes on one side. Don't peek! Let them brown!
Flip chicken thighs, and pour in broth. Scatter olives, lemon slices, garlic, capers, rosemary, thyme, fennel seeds, and, if using, anchovies over chicken.
Cover and lock the pressure cooker, making sure it's set to sealing. Set to High Pressure (or choose the meat feature) for 20 minutes. Allow a natural pressure release when cooking time is complete, about 10 minutes.
Uncover the Instant Pot, and remove the lemon slices. Transfer chicken to serving plates; loosely tent with foil.
Set the Instant Pot to Saute, and bring the sauce to a simmer, cooking until slightly thickened, 5 to 10 minutes.
Spoon the sauce over the chicken, and garnish with fresh thyme. Enjoy with couscous, or noodles. True comfort food!