Prepare barbecue (medium-high heat). Drain oil from feta into glass measuring cup. Whisk in oregano. Transfer 1/2 cup oil mixture to small bowl; whisk in 2 tablespoons vinegar. Season dressing with salt and pepper (reserve remaining oil mixture for brushing).
Brush chicken and onion wedges with reserved oil mixture; sprinkle with salt and pepper. Grill chicken until cooked through, 7 to 8 minutes per side, and onion until tender, 3 to 4 minutes per side. Transfer to cutting board; let rest 5 minutes.
Meanwhile, arrange spinach on large platter. Combine all tomatoes, olives, and feta in large bowl. Toss with enough dressing to coat generously. Season with salt and pepper. Arrange on platter with spinach.
Thinly slice chicken; arrange chicken and onion wedges on platter. Drizzle chicken and spinach with more dressing and serve.
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