Prepare a grill for medium-high heat; preheat 5 minutes (or heat a grill pan over medium-high heat). In a medium bowl, sprinkle chicken all over with oregano and coriander; season with salt and pepper. Add 2 Tbsp. oil, then toss to coat.

Grill chicken, covered, turning halfway through, until slightly charred and an instant-read thermometer inserted into thickest part registers 165°, about 8 minutes per side. Transfer to a cutting board, let rest 5 minutes, then thinly slice.

Meanwhile, in a small bowl, whisk vinegar, parsley, and remaining 5 Tbsp oil; season with salt and pepper.

Divide lettuce, cucumbers, avocado, tomatoes, olives, and feta among bowls. Top with chicken, then drizzle with dressing.