Season the chicken thighs with ½ teaspoon salt, pepper, oregano, and garlic powder.
Set the Instant Pot to Sauté. Add the olive oil, then sear the chicken for about 2 minutes per side. Transfer to a plate. The chicken does not need to be cooked through.
Add the garlic and cook for about 30 seconds. Pour in the chicken broth and scrape up any browned bits from the bottom of the pot. Turn off Sauté.
Stir in the rinsed rice, lemon zest, and remaining ½ teaspoon salt. Nestle the chicken thighs on top of the rice. Do not stir again.
Secure the lid and cook on High Pressure for 5 minutes. Allow the pressure to naturally release for 10 minutes, then carefully release the remaining pressure.
Transfer the chicken to a cutting board. Fluff the rice with a fork and stir in 2 tablespoons lemon juice, dill, and parsley.
Meanwhile, stir together the yogurt, remaining 1 tablespoon lemon juice, olive oil, garlic, and salt.
Serve the chicken over the lemon-herb rice with the lemon yogurt sauce. Enjoy!