In a compostable kitchen bag, combine the Icelandic yogurt, olive oil, lemon juice, lemon zest, garlic, and rosemary. Seal the bag and shake until combined.
If needed, pound flat the chicken pieces then season them with salt and pepper. Transfer them into the compostable bag and remove as much as from the bag as possible before sealing. Lay the bag flat and refrigerate until ready to use, no more than 12 hours.
Preheat your grill to a medium high heat. Using tongs, remove the chicken from the marinade and let any excess drip off. Place the chicken on the grill and cook until the chicken no longer sticks to the grill grate. Flip, and continue to cook until the internal temperature of the chicken reaches 165°F.
Remove and let the chicken rest for 5 minutes before serving.
Notes
For a beautiful presentation and extra flavor, grill extra lemon slices. They need 2-3 minutes per side to get grill marks.
Make a second batch of the marinade to use as a serving sauce on the chicken or for dipping bread into.