If you have a range you can just put the chicken under tented foil on top. The heat from the oven should be enough to keep it warm, but wouldn't it be easier to do a small turkey and only have one bird? You could cut it up to ease the cooking time.

Brine the chickens before roasting - it'll be super moist - then carve and keep in a low oven to keep warm. No biggie. Lay pieces out on a sheetpan so you don't lose that nice crisp skin and there's good air circulation.

Keeping chicken warm without drying it out can be tricky... Have you thought of using a different form of chicken? For example, cooking 3 flattened chickens simultaneously? You could probably fit all three in your oven at the same time. Or roasting chicken pieces? Either each chicken cut into 8 pieces (the French way of portioning a whole chicken creates 8 evenly-sized pieces, with the 2 wing tips leftover).

Personally, I would try a different menu if I couldn't fit all the meat in at one time; you are making your life terribly difficult when there are already lots of details to see to. If you want to stick to poultry, have you thought about roasting a stuffed turkey breast?

...ooops... either roast chickens cut in 8 equal pieces French fashion, or roast all thighs or all breasts...

pop it back in the over with just a tiny bit of hot broth/stock at the bottom of the pan to keep the meat moist but not so much that it gets soggy or that the skin doesn't crisp back up.

" then carve and keep in a low oven to keep warm."

You can't keep the first chicken in a low oven after carving if the oven is being used to roast chickens 2 and then 3. What do you do with the first chicken for approximately 2 hours? Tented foil won't solve the problem.

Two ideas:
Is your oven big enough to cook the chickens upright (beer can style)? The chickens will take up less area and might all fit in the oven at once. I've done two at a time this way, standing in a 9 x 13 lasagne dish. I suppose a bigger dish could hold three.

Precook and carve the birds, arrange the pieces on a cookie sheet in a low oven. Periodically mist the meat with chicken stock or white wine. This is a trick my mom uses. It isn't as good as a bird fresh from the oven but it's the best reheated bird I've had.

I would keep the chickens whole and tent them with foil. Carve them when it gets closer to dinner time. They will be lukewarm and the skin will have lost its crispiness, so spread the pieces on a baking sheet and stick them under the broiler until the skin begins to brown. The chicken will warm up but won't dry out. I just did this too : http://www.wittyinthecity.com/2012/02/perfect-roasted-chicken-with-gravy/

And your party sounds fabulous!

I definitely agree to make time to re-crisp the skin under the broiler, I'd also suggest a warm sauce/gravy to go along with them.

How do restaurants do it? Many restaurants serve roast chicken on their menu, and I'm sure they don't have 10 chickens being held at the right temp all night; and I can't imagine they could cook to order in enough time, so they must have some way of pre-cooking and then finishing to order to get the skin crispy...

I cook and carve turkey the day before Thanksgiving and layer the slices in a oven proof pan. I put iceberg lettuce leaves in the bottom of the pan and after drizzling some of the juices over the turkey I cover the slices with more ice berg lettuce and then foil. On the day, I reheat in a 350 degree oven till warm -- 30 minutes or so. The moisture in the lettuce leaves keeps everything from drying out. This is how the caterers I know reheat meat. Should work for chicken as well.

@Delta980 - most restaurants roast all of their chickens ahead of time and reheat each serving in a hot hot oven as orders come in.

After thanksgiving, I reheat leftover turkey in the toaster oven, covered by foil with some of the juices poured over. Helps keep everything nice and moist.

You don't want to keep chicken sitting warm for very long. Either cook ahead of time, refrigerate and then reheat, or serve it while it's still hot. Otherwise you are asking for trouble, food poisoning-wise.

If it were me doing this, I would roast and carve the chickens the day before, then heat them up in the oven the day of. I liked Famous Amos's tip about misting with wine or stock while you are warming them.