Combine chicken with olive oil, lemon juice, balsamic vinegar, spices, garlic, salt, and pepper in a bowl. Refrigerate for 20-30 minutes to marinate (or don't, if you're short on time. It'll still be great).
Toss potatoes and peppers with additional oil on a baking sheet, then season well.
Arrange the marinated chicken on top of the vegetables and transfer the Greek sheet pan chicken to the oven.
Cook your fast and healthy Greek sheet pan chicken until the chicken and vegetables are thoroughly cooked and golden.
While the sheet pan chicken cooks, mix chopped chili pepper, olives, and crumbled feta in a bowl. In another bowl, combine yogurt with extra garlic and salt.
Serve your fast and healthy Greek sheet pan chicken in warmed bowls. Scatter with the feta and olive mixture, and drizzle yogurt dressing over the top. Yummmm.