Make dressing: In a large bowl, combine oil, vinegar, garlic, salt, and pepper. Stir in thyme and cilantro, if using. Add paprika if you like.
Make salad: Set aside 1/2 cup dressing. Toss the rest in a large bowl with chicken. Let stand 10 minutes. Add vegetables and salad greens and toss with as much of the reserved dressing as you like.