In a large bowl, whisk together 2 tablespoons olive oil, dried oregano, minced garlic, half of the lemon juice, salt, and pepper.
Add the cubed chicken to the marinade and refrigerate for 15 to 30 minutes.
In a medium saucepan, combine the rinsed rice and chicken broth; bring to a boil, then reduce heat to low, cover, and simmer for 15-18 minutes until tender.
Heat a large non-stick skillet over medium-high heat. Add chicken and cook for 8-10 minutes, stirring occasionally, until the internal temperature reaches 165°F (74°C).
In a small mixing bowl, toss the tomatoes, cucumber, and red onion with the remaining 1 tablespoon of olive oil and the remaining lemon juice.
Assemble the bowls by layering a base of cooked rice followed by the grilled chicken and the vegetable salad mixture.
Top each bowl with kalamata olives, crumbled feta cheese, and a generous dollop of tzatziki sauce.