Toss chicken thighs with olive oil to coat. Select the browning or sauté setting and when hot, add 4 thighs to the pot. Brown three to four minutes on each side. Remove to a large bowl and repeat with the rest of the thighs. When you get to the last round of chicken thighs, toss the chopped onions in there and let it sauté with the thighs. When you remove the last of the chicken, leave the onions in there.
Once all the chicken is browned and in the bowl, add pesto to the chicken and toss it about to coat. Add chicken stock to the pot and give a little stir, making sure there are no brown bits stuck to the bottom. (Deglaze your pot.)
Insert the trivet into the pot and add the pesto coated chicken on the trivet. Top with potatoes and carrots.
Cook on high pressure for 12 minutes. When done, use quick pressure release. When pressure is released, remove lid carefully.
I like to remove the veggies and chicken on to a serving dish. It makes it much easier to serve since the veggies are all on top of the chicken. Serve with rice, polenta, or even mashed potatoes.
Before anyone freaks out about the quick release of the pressure and meat, please, relax. You can quick release meat. Trust me. There will be no negative outcomes to quick release. You will actually have a negative outcome if you let it come down naturally. You have carrots and potatoes in there that don't want to hang out any longer than necessary. Don't abuse your veggies. The meat is incredibly tender and moist.