I love this holy trinity of food, and until now, have only found it combined in Chicken, Broccoli and Cheddar Cheese Hot Pockets. However, I want some sort of entree deal out of it. So here’s your challenge: Make a recipe combining these three ingredients, with some stipulations. The dish has to have the flavors of the three ingredients featured prominently. It has to be enough for four to eat. And preferrably, very little to no carbohydrates, so Dad can eat it. Extra points if it includes a cheese sauce, as I have a dynamite recipe for it already. Also, all three ingredients must be present in each bite of the food.
Go, Iron Chefs!
Chicken, broccoli, cheddar casserole. My kids love it.
I’m embarrased that I can’t find it right now, so from memory:
Boil 4-5 boneless, skinless breast halves with a bay leaf for 15 min. or til cooked. Cool. Dice into bite sized cubes.
Cook broccoli until just barely done. Almost underdone. Drain.
MIx can of Creme of chicken soup and can of creme of mushroom soup(or creme of celery) in bowl with 1/2 cup of mayo. Also 1 tsp. of lemon juice.
Combine all the above in buttered casserole dish, probably about a qt. and a half size. Top with buttered bread crumbs(optional) and grated cheddar cheese.(lots). bake in 350 over for 20-30 minutes.
Kinda a version of chicken divan. Low-brow style.
Damn Red_Dragon you inadvertently stole my idea for a cooking game in IMHO, oh well, maybe I’ll do it anyway. 
Heck, I can think of several things for you, but I think I have a great one. A place I used to cook at served this: Grill up a chicken breast, top with steamed broccoli and cheese sauce. That’s it. Simple, quick, easy, damn tasty, and meets all your requirements.
Otherwise; maybe throw some diced roasted chicken and chopped broccoli in beer cheese soup? Sauté a chicken breast, and top with cheese and broccoli on a bun for a sandwich? I’d suggest mixing it with rice, but there are a lot of carbs there. Or even bake it into a good mac and cheese.
If you aren’t comfortable winging it, or are time crunched, adapt what you have. Campbell’s I believe makes broccoli cheese soup, toss in some cooked chicken.
Throw some chicken and some steamed broccoli in that boxed mac and cheese.
I believe most of those Rice a Roni type things have a broccoli and cheese variant, but there are a lot of carbs there.
Start slow, experiment, and enjoy.
ooh and on preview, what samclem said
I hope this isn’t the hot pockets you mentioned:
Cut a pocket into the chicken breast (cut in from the side). Stuff the pocket with shredded cheese and chopped, blanched brocolli. Close with toothpicks and saute.
Dammit, Manduck, you sort of beat me to it. I was going to suggest a Chicken-Kiev-type approach. Rather than cut a pocket into the breast, how bout this: Pound the breast down so it’s pretty flat and able to be rolled-up. Chop up some broccoli (blanched, per Manduck’s suggestion might be a good idea) and a rectangular wedge of cheese. Roll the chicken around the filling. Roll the chicken in some flour, then some beaten egg, and then some bread crumbs (you know, like making fried chicken.) Fry it in plenty of oil or, if you’re more health-conscious, bake.
Or, slightly more unimaginative but works with your cheese sauce suggestion. How bout a grilled chicken with broccoli and cheese sauce? Make yourself a bechamel by melting 3 tablespoons of butter. Add 3 tablespoons of flour. Let it cook for a couple of minutes. Add about a cup of milk or half-and-half or even light cream. Heat it for a bit and it’ll begin to congeal. Add a teaspoon of dry mustard, a cup of shredded cheese, salt and pepper. I’m trying to figure out how to handle the broccoli. I reckon you can probably cook it in the sauce, just don’t let the milk boil. Finely chop it and stick it in. Else you can cook it separately and then combine. Pour over the grilled chicken.