In a small bowl, combine paprika, chili powder, garlic powder, salt, pepper, dried oregano, and fresh lime juice to create a flavorful paste. Pat the chicken strips dry with paper towels, then rub the spice mixture evenly over all surfaces of each piece. This helps the seasonings adhere better and promotes better browning on the grill. Let the chicken sit for at least 10 minutes while you prepare your other components—this allows the flavors to penetrate the meat.
Heat a grill pan or outdoor grill to medium-high heat (around 375-400°F) and lightly coat with the olive oil. Once the grill is hot, carefully place the seasoned chicken strips on the grill, making sure not to overcrowd the pan—work in batches if needed. Grill for 6-8 minutes per side, depending on thickness, until the chicken reaches an internal temperature of 165°F when checked with a meat thermometer. I find that a grill pan works beautifully for this because it creates nice char marks while keeping the kitchen cooler than an outdoor grill.
Transfer the cooked chicken to a clean cutting board and let it rest for 5 minutes without cutting—this allows the juices to redistribute throughout the meat, keeping it tender and moist. After resting, slice the chicken strips into bite-sized pieces (roughly 1-2 inches) that will be easy to eat in the wrap.
Lay out one tortilla and arrange 2 lettuce leaves down the center to create a barrier that prevents the tortilla from getting soggy. Layer the sliced chicken from Step 3, then add about 1/4 cup of shredded cheddar and 2 tablespoons of ranch dressing on top. Fold in the sides of the tortilla first, then roll tightly from the bottom up, tucking as you go to create a secure wrap. Repeat with the remaining three tortillas. I like to shred my cheddar fresh from a block because pre-shredded cheese has anti-caking agents that prevent it from melting as smoothly.
Heat the same grill pan or a skillet over medium heat and lightly oil the surface. Place each assembled wrap seam-side down on the hot pan and cook for 1-2 minutes until the exterior is golden and slightly crispy, then carefully flip and toast the other side for another 1-2 minutes. The heat will warm the filling and help the cheese begin to melt slightly while creating a pleasant textured crust on the outside. Transfer the wraps to a cutting board, cut each one in half diagonally for an attractive presentation, and serve immediately while they're still warm.