Place the chicken thighs in a shallow dish, skin-side up. Combine the Greek seasoning, olive oil, and lemon juice; pour over chicken. Cover and refrigerate 1 hour.
Grill or broil the chicken over high heat for 10 minutes on each side, or until cooked through. Brush the zucchini with olive oil and grill 3-5 minutes per side, or until soft.
While the chicken cooks, combine the chopped cucumber and tomato. Season with salt and pepper.
Make the tzatziki by combining the yogurt, shredded zucchini, vinegar, 1 teaspoon olive oil, garlic, and dill. Season to taste with salt.
Serve the chicken, zucchini, tomato cucumber salad, and tzatziki over rice.