Whisk together the olive oil, lemon juice, lemon zest, minced garlic, oregano, smoked paprika, salt, and pepper in a medium bowl to make the marinade.
Place the chicken thighs in a shallow dish or resealable bag and pour half of the marinade over them, reserving the rest for brushing. Toss to coat, press out excess air if using a bag, and let sit at room temperature for 15–20 minutes (or refrigerate up to 2 hours).
While the chicken marinates, make the tzatziki: combine the Greek yogurt, grated drained cucumber, lemon juice, minced garlic, chopped dill, salt, and olive oil. Stir until smooth, taste and adjust seasoning, then chill in the fridge.
Heat a large skillet over medium-high heat. Add a drizzle of oil, then sear the marinated chicken (discard any leftover marinade that contacted raw chicken) for 5–7 minutes per side, depending on thickness, until an instant-read thermometer registers 165°F. Turn the heat down if the exterior is browning too quickly.
Transfer the cooked chicken to a cutting board and let it rest for 5 minutes, then slice into strips or bite-size pieces. Brush with the reserved marinade warmed briefly in the pan if desired for extra gloss.
Assemble the bowls: divide the warm rice or quinoa between four bowls. Top each with sliced chicken, cherry tomatoes, diced cucumber, red onion, Kalamata olives, and crumbled feta. Spoon a generous dollop of tzatziki over each bowl.
Finish with a sprinkle of chopped parsley, a drizzle of olive oil and a lemon wedge on the side. Serve immediately while the chicken and grains are still warm.