Place a skillet over medium heat and warm the tortillas for about 30 seconds on each side until flexible; set aside.
In a mixing bowl, combine shredded chicken, shredded cheese, and lime juice; stir until well mixed.
1 cup shredded cooked chicken
Scoop about 2-3 tablespoons of the chicken mixture onto the center of each tortilla.
1 cup shredded cooked chicken
Fold the sides of each tortilla over the filling and roll tightly to enclose the filling completely, sealing the edge with a light press.
Heat vegetable oil in a skillet over medium-high heat. Place the rolled chimichangas seam side down and cook for about 2-3 minutes until golden brown and crispy, then flip and cook the other side for another 2-3 minutes.
1 cup shredded cooked chicken
Remove from skillet and drain on paper towels. Serve immediately with desired accompaniments.