Marinate the chicken. Toss the sliced chicken with the yogurt, olive oil, lemon juice, garlic, oregano, paprika, salt, and pepper until every piece is coated. Let it sit for at least 15 minutes while you make the tzatziki the lemon and yogurt work quickly, so a short marinade genuinely does something here.
Salt and squeeze the cucumber. Grate the cucumber onto a clean towel, toss it with the ½ teaspoon of salt, and let it sit for 10 minutes. Then gather the towel and wring it out hard you should get a surprising amount of liquid, often close to ¼ cup. This is the step that keeps the tzatziki thick: that water has to leave the cucumber somewhere, and if it doesn’t leave in the towel it leaves in the yogurt about fifteen minutes after you’ve assembled the gyro. Squeezing it out up front means the sauce you mix is the sauce you eat.
Mix the tzatziki. Stir the squeezed cucumber into the yogurt along with the lemon juice, grated garlic, dill, and olive oil. Taste and adjust salt. Refrigerate until you’re ready to assemble.
Get the pan hot. Heat a dry skillet over medium-high until it’s properly hot — the chicken already has oil in the marinade, so you don’t need to add more. Pro tip: cook the chicken in two batches rather than one crowded pan. Crowding drops the pan temperature and the chicken steams in its own marinade instead of charring.
Sear the chicken. Add half the chicken in a single layer and cook undisturbed for about 3 minutes, until the underside is browned and slightly charred at the edges. Stir and cook another 2–3 minutes, until the chicken is opaque throughout and reaches 165°F internally. Repeat with the second batch.
Warm the pitas. Wipe out the skillet and warm each pita for about 20 seconds per side, just until soft and pliable with a few toasted spots. A cold pita cracks when you fold it; a warm one doesn’t.
Assemble. Spread tzatziki down the center of each pita, pile on the chicken, then add lettuce, tomatoes, and red onion. Fold and serve right away.