Step 1: Whip up the Marinade: In a medium bowl, whisk together the olive oil, lemon juice, minced garlic, dried oregano, salt, and black pepper. Taste and adjust seasoning if needed.
Step 2: Marinate the Chicken: Cut your chicken breast into thin strips (about 1/2 inch thick). Add the chicken strips to the bowl with the marinade and toss to coat well. Cover and refrigerate for at least 30 minutes (up to 8 hours).
Step 3: Heat Things Up: Preheat your grill or a large skillet over medium-high heat while the chicken marinates or towards the end of the marinating time.
Step 4: Cook the Chicken: Add the marinated chicken strips to the hot grill or skillet in a single layer. Cook in batches if needed. Cook for about 5-7 minutes total, flipping halfway through, until opaque, cooked through, and golden-brown/charred.
Step 5: Warm Those Pitas: While the chicken rests for a minute, lightly warm your pita breads. You can do this on the grill (30 seconds per side), in a dry skillet, or wrapped in a damp paper towel in the microwave (20-30 seconds) until soft and pliable.
Step 6: Assemble Your Masterpiece: Open up a warm pita. Spoon tzatziki sauce inside. Pile in cooked chicken strips, chopped lettuce, diced tomatoes, and sliced red onion.
Step 7: Serve and Enjoy: Fold or wrap your gyro and serve immediately while warm.