Make the rice: In a medium saucepan, combine the chicken broth and rice and bring to a boil over high heat. Lower the heat to medium-low and simmer, covered, until the rice is cooked, 15 to 20 minutes (or 40 minutes if using brown rice). Set aside to cool. Make the salad: In a medium bowl, toss together the cucumbers, tomatoes, and olives. Add the feta, oil, lemon juice, salt, and pepper, and toss to combine. For the chicken: Heat the oil in a medium saucepan over medium heat. When the oil is shimmering, add the garlic and cook, stirring occasionally, until fragrant, 30 seconds. Add the chicken, lemon juice, rosemary, thyme, oregano, salt, and pepper, and toss to combine. Cook until the chicken is heated through, 5 minutes. Divide the rice, chicken, and salad among four bowls. Top with the tzatziki sauce.