I also never pre-cook potatoes when making a gratin - you just need to cook them long enough. You want to cook at a low enough temperature such that the potatoes cook through before they get too brown on the top. Alternatively you can use a lid to start, but this dish can be cooked uncovered at one temperature with cooked potatoes and a crispy top - it just depends on your gratin depth, oven, etc. I also suggest that you start it in a cold oven, allowing it to pre-heat with the oven.
Personally I wouldn't cook the chicken from raw in the gratin, as it will inevitably overcook and become rubbery (and it's likely not long enough of a cook time to break down all the collagen that makes it rubbery). If you cook the chicken in a pot with some water for a few hours, you could then break up the fall-apart tender meat to include in your uncooked gratin, and reduce the resulting stock to include as part of the cooking fluid with your milk/cream and BBQ sauce. Some broccoli in that would be good too I bet, along with the cheddar (sorry, I recoil from the foil pack of V).
Nick ~ "Egg whites are good for a lot of things; lemon meringue pie, angel food cake, and clogging up radiators." - MacGyver