In a large bowl, combine olive oil, red wine vinegar, lemon juice, minced garlic, oregano, salt, black pepper, paprika, and cumin. Whisk until well blended.
Add the chicken thighs to the marinade, ensuring they are fully coated. Cover and refrigerate for at least 1 hour, or up to overnight for best flavor.
Preheat your grill or grill pan over medium-high heat. Remove the chicken from the marinade and discard the marinade.
Grill the chicken for about 6-7 minutes per side, or until fully cooked and the internal temperature reaches 165°F.
Let the chicken rest for 5 minutes before slicing it into thin strips.
Warm the pita breads on the grill for about 1 minute on each side.
To assemble the gyros, place a generous amount of sliced chicken on each pita. Top with tzatziki sauce, sliced tomatoes, shredded lettuce, and red onion.
Roll up the pita and serve immediately.