Add the chicken breasts, salsa verde, diced jalapeño, chili powder, kosher salt, and black pepper to the Instant Pot. Do not add the Greek yogurt yet.
Secure the lid and ensure the vent is sealed. Set the Instant Pot to Manual (High Pressure) and cook for 15 minutes.
When the cooking time ends, allow a natural pressure release for 5 minutes, then carefully perform a quick release and open the lid.
Remove the chicken to a cutting board and shred with two forks or with tongs. Return the shredded chicken to the Instant Pot.
Stir in the plain Greek yogurt until the sauce is smooth. Switch the Instant Pot to Sauté and bring the mixture to a gentle simmer.
Simmer for about 5 minutes to warm through and slightly thicken the sauce, stirring occasionally.
Serve the creamy salsa verde chicken hot.