Line a large, rimmed baking sheet with paper towels and set a metal rack over the top; set aside.
In a large bowl, mix together the chicken, shredded cheese, diced tomatoes, lime juice, oregano, chili powder, cumin, salt, and pepper until everything is well combined. You should achieve a cohesive mixture that is fragrant and inviting.
In a deep skillet or Dutch oven, heat about ½ inch of vegetable oil to a temperature of 325°F to 350°F. Using a thermometer is helpful here; the oil should shimmer but not smoke.
While the oil is heating, take 4-5 of the corn tortillas and place them on a microwave-safe plate. Cover with a damp paper towel and microwave for 30 seconds on HIGH. Flip the stack and microwave for an additional 30 seconds. This makes them pliable for rolling.
Once softened, set one tortilla on a flat surface. Spoon about 2 tablespoons of the chicken mixture about 1 inch from one edge of the tortilla.
Form the filling into a tube shape and begin rolling the tortilla tightly starting from the edge closest to the filling. Secure it with toothpicks if needed. This helps maintain the shape while frying.
Repeat the rolling process with the remaining tortillas, making sure not to overfill them; this prevents tearing.
Fry 4-5 rolled tortillas at a time in the hot oil, seam side down, for about 3 to 5 minutes until they’re golden brown. Flip them halfway through to ensure even cooking.
Once they’re perfectly golden, use a slotted spoon to transfer the fried taquitos to the prepared metal rack, allowing excess oil to drain.
Continue frying the remaining rolled tortillas, keeping an eye on the oil temperature to ensure it remains at 350°F. This is key for achieving that crispy texture.
After frying, carefully remove the toothpicks from the taquitos and serve them hot alongside your favorite toppings like sour cream, guacamole, salsa, or cheese sauce.