Place 1 pound boneless skinless chicken breasts (2 large breasts) in a gallon-size resealable bag. Add 3 tablespoons olive oil, zest of 1 lemon, 2 tablespoons lemon juice, 2 cloves garlic (minced), 1 teaspoon dried oregano, 1/2 teaspoon kosher salt, 1/4 teaspoon black pepper, and a dash of crushed red pepper flakes. Seal the bag, press out excess air, and massage the marinade around the chicken. Marinate in the refrigerator for at least 30 minutes and up to 1 hour, turning the bag occasionally.
About 10 minutes before cooking, heat a grill or a grill pan to medium-high. Lightly brush the grill grates or the grill pan with olive oil to prevent sticking.
Remove the chicken from the bag and discard the marinade. Place the chicken on the preheated grill or grill pan. Grill about 5 minutes per side, adjusting time for thickness, until the chicken is no longer pink in the center and an instant-read thermometer inserted into the thickest part reads 165°F (74°C).
Transfer the chicken to a cutting board and let it rest for 5 minutes. Then slice the chicken thinly.
If using cold cooked cauliflower rice, regular rice, or quinoa (2 cups total), reheat now if desired. Divide the 2 cups of cooked cauliflower rice (or regular rice or quinoa) evenly among 4 bowls.
Top the rice in each bowl with the sliced chicken, 2 cups grape tomatoes (halved) distributed across the bowls, 2 cups chopped cucumber, 1 cup kalamata olives (pitted and sliced), and 1/2 red onion (sliced) divided among the bowls.
Add 1 cup tzatziki sauce to the bowls (as a dollop or spread) and sprinkle a total of 1/2 cup crumbled feta cheese over the bowls. Squeeze lemon wedges over each bowl to taste.
If using, tuck pita chips into the side of each bowl and garnish with fresh dill and parsley. Serve immediately.