Preheat the oven to 400°F (200°C).
In a mixing bowl combine the chicken with 2 tablespoons of the olive oil, tomato paste, smoked paprika, chopped garlic, lemon zest, chili flakes, and salt and black pepper to taste; toss to coat evenly.
Heat a large oven-safe skillet over high heat and add the remaining 1 tablespoon olive oil. Sear the chicken on both sides until golden, about 3–5 minutes total.
During the last 2 minutes of searing, add the butter to the pan. Remove the chicken to a plate, keeping the fond in the skillet.
Add the orzo and 2 tablespoons fresh thyme to the hot skillet and cook, stirring, until the orzo is lightly toasted, about 1 minute.
Stir in the chopped sun-dried tomatoes, chicken broth, and the 2 tablespoons lemon juice. Season with salt and pepper, then stir in the mixed fresh herbs (basil and thyme).
Return the seared chicken and any accumulated juices to the skillet, nestling pieces into the orzo mixture.
Bake the skillet uncovered in the preheated oven for about 15 minutes, or until the chicken is cooked through and the orzo is tender.
Remove from the oven and top the chicken and orzo with tzatziki sauce and additional basil if desired, then serve.