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.

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.

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.)

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.

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.