I came across this recipe on a search for "chicken" and "Mexican." It's too good to not pass along: http://www.bigoven.com/165050-Chi-Chi's-Baked-Chicken-Chimichangas-recipe.html
It meets my requirements to be quick, relatively simple and super tasty -- thumbs up from all 5 kids, even the two little ones who claim that they "don't like chicken," unless it's in the form of a nugget.
It's better than in the restaurant, if you ask me, because it's not all gloppy. We served it with mango salsa from Costco, which though it may not sound appetizing, really is.
I cooked the chicken then ran it through the food processor to "shred" it. I also didn't wait for it to cool down before spooning it into the tortillas.