In a small bowl, combine all marinade ingredients, except for the chicken, and mix well.
Place the chicken breasts into a large Ziploc bag or container, then pour the marinade mixture over them.
Allow it to marinate for 30 minutes to 1 hour, or overnight.
Preheat the oven to 375°F and line a baking sheet with foil.
Place the chicken on the baking sheet and bake for 25-30 minutes, until fully cooked.
Switch the oven to broil and move the chicken to the broil rack, cooking for an additional 5-10 minutes, until the internal temperature reaches 160°F and the chicken is browned and crispy in spots.
While the chicken cooks, rinse the rice several times until the water runs clear.
In a medium saucepan, combine the rice, salt, oregano, pepper, and water, then bring it to a boil.
Cover and reduce the heat to a simmer, cooking for 18 minutes.
After removing from heat, fluff the rice with a fork.
For the tzatziki sauce, grate the cucumber, squeeze out excess water using a towel, and mix all the sauce ingredients in a medium bowl.
To assemble the bowls, place a cup of rice in each bowl, top with the chicken and vegetables, and finish with tzatziki sauce.