Turn at least 2 of the burners on your grill to high heat and let it preheat for at least 10 minutes. Leave one side of the grill without any flame. I have a 3 burner grill, so I just leave one off. If you have a 2 burner grill, turn them both on high and then turn one off once you’ve got your nice grill marks. More on that later!
Add salsa verde ingredients to a high speed blender and blend until well combined (it will be a bit chunky), scraping the sides and under the blade as needed. Reserve ¼ cup and transfer the rest to a jar or small bowl to serve.
Add chicken parts to a large bowl and toss with the salt, pepper, and oil to coat.
Once the grill is preheated, add your chicken, skin-side-down, to the hot side of the grill, then cover and grill for 3-5 minutes or until you have nice grill marks. Flip and repeat on the other side. Transfer the chicken to the part of the grill with no heat and let it cook over indirect heat, covered, for 15-20 more minutes or until the internal temperature is at least 165F. Try not to peak - you want that grill to act like an oven.
Transfer the chicken to the bowl and pour the ¼ cup reserved salsa verde over top. Toss to coat. Cover with foil until ready to eat!
Serve the chicken on a platter drizzled with the salsa verde/chicken drippings at the bottom of the bowl. Serve with the remaining salsa verde on the side (it’s delicious on grilled veggies too!).