If using chicken breasts, cut the chicken in half horizontally to form thinner cutlets.
To marinate the chicken, in a medium bowl combine 3 tablespoons olive oil, 2 tablespoons lemon juice, garlic, ½ teaspoon oregano, dill, ½ teaspoon salt, and pepper. Add the chicken and toss well to coat. Refrigerate for at least 30 minutes or up to 3 hours.
For the rice, in a medium saucepan, combine rice and butter and cook, stirring over medium heat until lightly browned, about 5 minutes.
Add broth, the remaining 2 tablespoons lemon juice, ½ teaspoon oregano, and ½ teaspoon salt. Bring the rice to a boil over medium-high heat, cover, and reduce to a simmer. Cook for 15 to 20 minutes or until the liquid has been absorbed. Remove from the heat and let rest 5 minutes.
Remove the chicken from the marinade allowing excess to drip off and discard the marinade.
In a large 12-inch skillet, heat 1 tablespoon of oil over medium-high heat. Add the chicken and cook for 2 to 3 minutes per side or until it is cooked through and reaches 165°F in the thickest part. Transfer to a cutting board and let rest 5 minutes.
Slice the chicken into bite-sized pieces.
To assemble, fluff the rice with a fork and divide between four bowls. Top with the chicken, tzatziki, and toppings as desired.
