Make the marinade: whisk together 3 tbsp olive oil, 3 tbsp lemon juice, lemon zest, 3 minced garlic cloves, 2 tsp dried oregano, 1 tsp kosher salt and 1/2 tsp black pepper in a shallow bowl.
Trim and even out the chicken: if breasts are thick, slice them horizontally or lightly pound to about 1/2-inch thickness so they cook evenly. Add the chicken to the marinade, turning to coat. Let rest at room temperature for 10–15 minutes (or refrigerate up to 2 hours).
Cook the quinoa: while the chicken marinates, rinse 1 cup quinoa in a fine mesh sieve. Combine quinoa and 1 3/4 cups water (or broth) in a small saucepan, bring to a boil, then reduce to low, cover and simmer 12–15 minutes until water is absorbed. Remove from heat, fluff with a fork and stir in 1 tbsp olive oil and a pinch of salt.
Prepare the tzatziki: grate half the cucumber into a small bowl, squeeze out excess moisture using a towel or paper towel. Combine grated cucumber with 1/2 cup Greek yogurt, 1 minced garlic clove, 1 tbsp lemon juice and 1/4 tsp salt. Chill until assembly.
Sear the chicken: heat a large nonstick or cast-iron skillet over medium-high heat and add a drizzle of oil. Remove chicken from the marinade (shake off excess) and sear 5–7 minutes per side, lowering heat if the outside browns too quickly. Cook until an instant-read thermometer reads 165°F in the thickest part.
Rest and slice: transfer chicken to a cutting board and let it rest 5 minutes, then slice into strips or bite-sized pieces.
Assemble the bowls: divide the warm quinoa and greens between four bowls. Top each with sliced chicken, diced cucumber, halved cherry tomatoes, red onion, Kalamata olives and crumbled feta.
Finish and serve: dollop 2 tbsp of tzatziki per bowl (or more to taste). If desired, squeeze additional lemon over the top and sprinkle a pinch more oregano. Serve immediately.