If I had a leftover chicken right now, I’d make chicken noodle soup with it. It doesn’t take anything but broth, spices, carrots, onion, celery, and whatever kind of noodles you like.
Or I’d make chicken salad, but right now I’m too cold for that.
/edit: I’m late! Good idea!
Easiest chicken recipe for cooked chicken:
Chicken
can of great northern beans
salsa (hot salsa works well for this)
cream cheese or sour cream
Throw the first three together in a pan. Heat. Add the amount of cream cheese you want. Melt. Serve. If it’s sour cream, take the pan off the heat, stir in sour cream. Serve.
You can leave out the dairy if you prefer.
I can’t seem to find it anymore, but Zatarain’s used to make something called “chicken creole rice mix” that was absolutely perfect for leftover chicken. Just cut up the chicken and dump it in with the mix and let it simmer for half an hour, and dinner is served!
Creamed Chicken and Biscuits (by “no special trip to the store”, I’m hoping you mean you have some frozen veggies and refrigerated/frozen biscuits on hand, right?)
Put chicken in a large oven-proof skillet (or regular skillet, which you may transfer to casserole dish later); pre-heat oven to 350 (or whatever the package directions on the biscuits call for). Stir a can of cream of chicken soup (cream of mushroom may be substituted) plus a half-can of milk into pan, heat to simmering; add half a bag of mixed frozen veggies, or frozen peas and carrots; return to simmer. Top with biscuits, bake as long as the biscuit package says, or until the biscuits on top are golden. Brush biscuits with butter. Serve in bowls.
Variation: for Creamed Chicken and Dumplings: do not pre-heat oven; follow directions as above, but after putting the refrigerated or frozen biscuits on top, turn heat to low, cover tightly and allow the biscuits to steam, thereby making dumplings as opposed to biscuits.
Mmmmm. Now I’m hungry.
Buffalo Chicken Sloppy Joes
Melt 3 or 4 tablespoons of butter, add hot sauce to your liking, maybe a tablespoon or two of tomato paste if you have some – it’s not essential. Dump in the chunked or shredded cooked chicken and toss together until warm. Spoon onto toasted buns and top with bleu cheese crumbles (available at the deli or salad bar in the grocery store).
My kid concocted this based on a Rachael Ray recipe. It’s incredibly easy and really good.
Damn it, I have chicken soup simmering. I would have much rather made Alpine’s “Tuscan Chicken Pasta” - it sounds great, and it wouldn’t have even needed a trip to the store.
My dad wanted me to come over for dinner the other night and he said he had some leftover chicken. I said “ugh, I don’t want just chicken.” He offered to make me cream chicken. I think he was done with it in about 15 mins. I like mine over toast or rice.
I’ll be damned if I actually know how to make it, tho. It’s been one of my favorite “comfort foods” for 30 years!!
Normal people call it chicken a la king 
Even tho it has the same name, it’s not like norinew’s recipe. The sauce is only butter, milk and flour I think (probably salt & pepper too). All of the other chicken a la king recipes have stuff like mushrooms and pepper and chicken broth.
I suppose I should ask my parents how to make it someday. But then, what would I go home to?
No one’s mentioned curry?
Chicken curry, every time.
I’ve no doubt that my “recipe” is a bastardized short-cut version of some real recipe that calls for cooking an actual sauce. 
You can ask your parents for their recipe, work on ‘perfecting’ it at home, but still go home to theirs. I guarantee you can follow their recipe to the letter (although if they cook like me, their recipes don’t have a ‘to the letter’ because it’s more like ‘a little of this until it smells right. . .’) and it will not taste like theirs. My grown daughters attempt my recipes, and swear theirs never comes out like mine. Of course, because of my slap-dash style of cooking, my recipes seldom come out like mine.
Put it down my pants. Squishy.
Slice up the leftover chicken. Make mashed potatoes with plenty of butter and black pepper. Make mushroom gravy (one chopped onion, sliced mushrooms, garlic, olive oil in hottish pan. Chicken stock powder. Cook onions until beginning to be golden, throw in a teaspoon of plain flour to make a roux with the olive oil (yes, I know). Cook out, then throw in simultaneously wine or sherry and a handful of dried brown mushrooms. Cook off alcohol, then make the gravy up to the consistency you want with water). While you finish the gravy, heat up some frozen peas - and lo, a five minute meal that’s actually balanced!
Buffalo Chicken Dip
Chop up the cooked chicken and layerit in the bottom of a 9x13 casserole dish. Drizzle with the buffalo wing sauce of your choice. Mix together one 24 oz bottle of ranch dressing with 2 blocks of softened cream cheese and spread over the chicken. Top with shredded cheddar cheese and bake at 350 degrees until the cheese is melted and bubbly. Serve with tortilla chips or Fritos and try not to pig out!
A big favorite here:
http://www.epicurious.com/recipes/food/views/Tex-Mex-Sheperds-Pie-103138
Though it might call for ingredients you don’t have on hand. The cheese for example, though I’d bet you can make do with that with swiss or regular Monterey Jack, with some green chilies thrown in.
Insanely easy, really. We buy the premade mashed potatoes (near the rotisserie chicken) when we’re expecting to make this. Usually I’m using up the meat from a leftover turkey breast, not chicken though.
I bought a rotisserie chicken to make chicken quesadillas, put into pita bread with hummus and roasted peppers, and use in tossed salad with avocado and other assorted veg. The last meaty bits go into Ramen noodles.