In a large bowl, mix together cream cheese, shredded cheese, tomatoes, cumin, cayenne pepper and lime juice. Fold in chicken and season with salt & black pepper. Refrigerate until ready to use.
Line a large, rimmed baking sheet with foil and insert a metal rack; set near the stove.
Heat ½-inch oil in a Dutch oven or deep skillet to 325°F-350°F.
When the oil is almost ready, place 6 tortillas on a microwave-safe plate and cover with a clean, damp cloth. Microwave 30 seconds on HIGH, flip the stack of tortillas over, cover with the damp cloth and microwave an additional 30 seconds.
Remove 1 tortilla (keep the remaining tortillas covered). Set the tortilla on a flat surface and place 2 tablespoons chicken/cheese filling mixture 1-inch from one edge of the tortilla. Form the filling into a tube-shape and, beginning at the edge closest to the filling, tightly roll up the tortilla.
When the oil is ready, use tongs to set the tortilla, seam-side down, in the oil. Hold the Taquito, at the seam, with the tongs to keep the tortilla from opening up until the tortilla stays closed. Cook until golden brown on the bottom side then flip the Taquito over to fry the other side. Transfer to the prepared metal rack. Repeat the process with the remaining 5 warm tortillas.
After the first six Taquitos have been made, repeat the process of warming, filling and frying the Taquitos.
Serve with your favorite toppings, and enjoy!