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Step 1
Select SAUTÉ setting on a programmable pressure cooker (such as Instant Pot). (NOTE: Times, instructions, and settings may vary according to cooker brand or model.) Select HIGH temperature setting and allow to preheat 3 minutes. Meanwhile, remove skin from chicken by slipping fingers under the skin and pulling it off; discard skin, and pat chicken dry. Stir together salt, pepper, and oregano in a small bowl; sprinkle evenly over all sides of chicken. Add oil to cooker. Working in batches, add 3 or 4 chicken thighs to cooker. Cook until golden brown on bottoms, about 5 minutes; flip and cook until other side is browned, about 3 minutes. Transfer thighs to a plate. Repeat process with remaining thighs.
Step 2
Add stock to cooker, stirring to loosen browned bits. Place metal wire steam rack in cooker. Place browned chicken thighs on steam rack; pour any accumulated drippings from plate into cooker.
Step 3
Press CANCEL. Cover cooker with lid, and lock in place. Turn steam release handle to SEALING position. Select MANUAL/PRESSURE COOK setting. Select HIGH pressure for 12 minutes. (It will take 8 to 10 minutes for cooker to come up to pressure before cooking begins.)
Step 4
Carefully turn steam release handle to VENTING position, and let steam fully escape (float valve will drop). (This will take 3 to 4 minutes.) Remove lid from cooker.
Step 5
Transfer chicken to a platter. Remove steam rack from cooker. Select SAUTÉ setting on cooker; select HIGH temperature setting. Let stock mixture come to a boil. Stir together cornstarch and cold water in a small bowl; whisk into boiling stock mixture. Cook, whisking constantly, until mixture thickens, about 1 minute. Stir in lemon zest and juice, parsley, and chives. Pour gravy evenly over chicken thighs.