Combine cilantro, parsley, garlic, cumin, paprika, salt, and cayenne pepper in a food processor.

Process the ingredients until they are finely pureed.

Gradually add olive oil through the feed tube while the machine is running, blending until the mixture is smooth.

Transfer 1/4 cup of the herb mixture to a small bowl and reserve for later.

Add yogurt and lemon juice to the remaining mixture in the food processor.

Blend until well combined.

Place the chicken breasts in a 13x9x2-inch glass baking dish.

Pour the yogurt mixture over the chicken, ensuring each piece is thoroughly coated.

Cover the dish and refrigerate for at least 1 hour, or up to 5 hours, to allow the chicken to marinate.

Preheat the barbecue grill to medium heat.

Place the marinated chicken breasts on the grill, skin side down.

Cover the grill and cook the chicken for about 20 minutes, turning every 5 minutes, until the chicken is cooked through and no longer pink inside.