In a medium-sized bowl, combine the Greek yogurt with olive oil, minced garlic, lime juice and zest.
Season the marinade with oregano, paprika, salt, and pepper.
Mix everything well until you have a smooth marinade sauce.
Add the chicken breasts (or thighs) to the bowl, making sure they are fully coated in the yogurt marinade.
Cover the bowl with plastic wrap or transfer the chicken to a resealable plastic bag.
Refrigerate for at least 1 hour, preferably overnight, to let the flavors penetrate the chicken.
Once marinated, remove the chicken from the fridge and let it sit at room temperature for 15 minutes before cooking.
Heat a grill, grill pan, or skillet over medium-high heat.
Cook the chicken for 5-7 minutes per side, or until the internal temperature reaches 165°F (75°C), and the chicken is fully cooked through.
Garnish with fresh parsley, slice, and serve with your favorite side dishes.