Start by preparing all your components so you can focus on cooking once the heat is on. Grate the cucumber on the large holes of a box grater, then wrap it in a clean kitchen towel and squeeze out all excess moisture—this prevents a watery tzatziki. Mince the garlic clove very finely, chop the fresh dill, and juice the lemon. In a medium bowl, combine the Greek yogurt, grated cucumber, minced garlic, fresh dill, and fresh lemon juice with a pinch of salt. Stir until smooth and set aside in the refrigerator. For the salad components, dice the tomatoes into ½-inch pieces, dice the English cucumber, and finely mince the red onion. Set these aside in separate bowls. I like to prep the tzatziki first while the kitchen is calm—it actually tastes better when it sits for a few minutes and the flavors marry together.
In a small bowl, combine 2 tablespoons of the dried oregano with the paprika, cumin, garlic powder, 1.5 teaspoons salt, black pepper, and red pepper flakes. Cut your chicken thighs into 1-inch chunks and generously coat them with this spice mixture on all sides. Heat 3 tablespoons of olive oil in a large skillet or Dutch oven over medium-high heat until shimmering. Working in batches if needed to avoid overcrowding, sear the chicken for 3-4 minutes per side until deeply browned. Transfer the browned chicken to a clean bowl—you're looking for color and caramelization here, which builds flavor for the whole dish. Don't worry about cooking the chicken through; it will finish cooking in the broth.
In the same skillet with the browned bits (fond) still clinging to the bottom, heat the remaining 1 tablespoon of olive oil over medium heat. Dice the medium white onion and add it to the pan, cooking for 2 minutes until just softened and fragrant. Add the rice and stir constantly for about 1 minute to lightly toast the grains and coat them with oil—this gives the rice better texture and prevents mushiness. In a separate container, whisk together the 2 cups of chicken broth with the remaining 0.5 tablespoon of dried oregano and the zest from the lemon. Pour this broth mixture over the rice and stir once, then place the seared chicken from Step 2 on top of the rice (don't stir it in). Increase the heat to medium-high until the liquid comes to a boil, then cover the pan tightly with a lid.
Once the broth reaches a boil, reduce the heat to medium and maintain a gentle simmer. Cover and cook for exactly 20 minutes without lifting the lid or stirring—the steam will cook the rice perfectly and the chicken will become tender and infused with the oregano and lemon flavors. After 20 minutes, remove from heat and let it sit covered for 2-3 minutes. Fluff the entire mixture gently with a fork to separate the rice grains and distribute the chicken throughout. The rice should be tender, the liquid absorbed, and the chicken fully cooked through.
Transfer the fluffed rice and chicken mixture to serving bowls or a large platter. Scatter the fresh parsley over the top, which adds brightness and color. Arrange the diced tomatoes, diced cucumber, feta cheese crumbles, and minced red onion on the side or mixed into the rice, creating a fresh Greek salad component right in the bowl. Spoon a generous dollop of the chilled tzatziki from Step 1 over the top or on the side. Warm the pita bread and serve alongside with lemon wedges for squeezing over everything at the table. I always warm my pita just before serving—it makes it much more pleasant to eat and helps it hold the filling better if you want to build little wraps with it.