In a gallon sized zip-top bag or airtight container, add the yogurt, lemon juice, dried oregano, and avocado oil. Mix the marinade ingredients in the bag until combined.
Add chicken breasts. Massage the marinade to coat the chicken.
Marinate the chicken for as little as 30 minutes up to 24 hours in the refrigerator.
Preheat the grill to medium heat. Shake off any excess marinade and place the chicken on the grill. Cook the chicken until its internal temperature reaches 165°F.
Allow chicken to rest for five minutes before slicing.