This is not truly an authentic Mexican item in itself, rather a combination of cooking styles combined to make a great entree. I came up with this many years ago when I had free run of the mexican restaurant I was managing, and it was a big hit with my employees, and my family.
2 boneless skinless chicken breasts
2 pkg fajita seasoning (use your favorite brand)
2 green bell peppers
1 medium yellow onion
1 1/2 cups apple cider vinegar
4 1/2 cups vegetable oil
lettuce
sour cream
cheddar cheese
tomatoes
sliced black olives
tooth picks
oil for deep frying
Trim the chicken breasts of any excess fat. Slice them widthwise (the short way) into thin strips, about 1/4" or so. Core the peppers, halve, and cut into strips. Peel and cut the onion into strips. Ready two mixing bowls, one medium and one large. Place one package of fajita seasoning mix into each bowl. In the medium bowl place 1/2 cup of cider vinegar, and 1 1/2 cups of vegetable oil. In the large, place the remaining 1 cup of cider vinegar and 3 cups of oil. Whisk both to combine the spices and slightly emulsify the marinade. Place the chicken in the medium bowl, and the peppers and onions in the large one. Stir again to combine. Place the chicken and vegetables into separate tupperware containers and refrigerate 2 to 4 hours, or overnight (The chicken will last 4 days refrigerated in the marinade). Place the vegetables into a large enough container where you can shake them occasionally. When you first place the vegetables in the marinade they will be stiff, but after marinating overnight, they will become limp and take up less space.
Place a good sized wok or a large pan with sloping or high sides over high heat. Now is a good time to turn on your overhead fan in the kitchen 
When the pan is very hot, place the chicken into it using a slotted spoon. Drain off some marinade, but leave a little in each spoonful for flavoring.
NOTE: I have an electric stove at home, however most restaurants use gas as it is cheaper. We not only left some marinade in for flavor, but it also makes an impressive display in the dining room, as the high heat and gas flame causes it to light on fire. If you are UNFAMILIAR with cooking with a flaming pan, the time to learn is not now. adjust the heat a bit lower and drain off as much marinade as you can. While there is no real danger from the flames as they only last for a few seconds of shaking, a suprised cook is liable to do anything, so please use caution if you have gas burners.
Cook the meat, stirring until chicken is slightly browned or blackened and cooked through, about 3 to 5 minutes. Remove chicken and drain pan of excess marinade. Allow it to reheat for a few minutes and repeat the process with the vegetables. I cook mine until they are on the blacker side, but you can cook them to your tastes. Remove peppers and onions and reserve in a bowl.
Heat your deep fryer to 375 degrees, or place oil in a large pan with high sides to a depth of about 3 inches and heat to 375. Divide the chicken and the peppers and onions into four equal parts. Take the flour tortillas, one at a time, and run them under your sink spout with the water just barely running in a continuous stream. (This helps them to steam in the microwave instead of getting brittle). Place in the microwave on high for about 25 seconds. Remove tortilla and spread with sour cream. Then sprinkle with cheddar cheese. Next, place 1/4 of the chicken mixture and 1/4 of the pepper and onion mixture on the cheese, in the center of the tortilla. Top with lettuce, tomatoes, and black olives (all fillings subject to the quantities you desire). Now you simply roll them up and pick them closed. Grab the tortilla by the edge closest to you, and fold it over to the edge farthest away. making a half moon. Slowly drag the top part back towards the center with both hands, where the filling is, until you can feel the filling against the tortilla. Don’t pull too far or it’ll squirt out the sides. Right now it should look like a half rolled enchalada. Starting with the left side (ir right side if your’re right handed) fold the edge in towards the filling, so that it is pointing towards the top of the roll and keeping the filling from coming out. Repeat this on the opposite side. Now simply roll it over away from you until the bottom part of the tortilla meets the rest of the chimichanga, like sealing an envelope flap. Now place enough toothpicks along the seam to keep it sealed tight while cooking. It may sound somplicated, but the whole process from rolling through picking only takes about 20 seconds once you get used to it. Repeat this for the rest of the tortillas Fry them in the oil, turning to ensure even cooking, until they are golden brown. The filling is already cooked, so you just want to fry the tortilla here. Drain them on paper towels. I serve them covered with the cheese sauce from one of my previous posts, along with spanish rice and refried beans.
For a change up, you can substitute beef burrito or taco filling, or even chili, in place of the fajitas. Top it with enchilada sauce and cheddar cheese, or, you can top it with ranchero sauce and cheese for a little extra kick. Hope you enjoy!