Combine olive oil, lemon zest, lemon juice, Dijon, garlic, dried oregano, dried basil, salt and pepper in a bowl or large zip-top plastic bag. Whisk or squeeze bag to mix.
Pound the chicken breasts to an even ¾-inch thickness before adding them to the marinade. This helps them to cook evenly and also tenderizes the meat. Place chicken breasts in a zip-top bag or between two layers of parchment paper or plastic wrap and use a rolling pin or meat mallet to pound the chicken.
Add the chicken to the bag or bowl and coat with marinade. Refrigerate for at least 30 minutes and up to 12 hours. I usually aim to marinate chicken for 1-4 hours.
To Cook Chicken on the Grill: Clean the grates of a gas or charcoal grill. Oil the grill grates and heat the grill to medium-high (375-450 degrees F). Discard used marinade and grill chicken breasts for 5-8 minutes per side, until cooked through to an internal temperature of 165° F. Let chicken rest for 5 minutes before slicing and serving.
To Cook Chicken on the Stove: Heat 1 tablespoon of olive oil in a large heavy skillet (such as a cast iron skillet) over medium-high heat. Discard used marinade and add the chicken to the pan. Cook chicken breasts for about 5-8 minutes per side, or until chicken is cooked through to an internal temperature of 165° F. Let rest for 5 minutes before slicing and serving.
Assemble bowls: Divide the lettuce and cooked rice between 4 serving bowls. Add sliced cooked chicken, tomatoes, cucumber, red onion, kalamata olives, and a spoonful of tzatziki or hummus or a drizzle of tahini sauce. Finish with crumbled feta and chopped fresh herbs. Serve immediately.