Yes, the traditional Christmas goose (or Hanukkah goose, or Kwanza goose, or just plain old winter solstice goose) is Paleo-friendly. Americans have largely gotten away from goose in favor of the more lean meats of chicken and turkey. Although all birds can constitute a nutrient-dense Paleo meal, you should definitely go for the goose, if you can get your hands on it.
The Benefits of Fat
In addition to all the micronutrients normally found in meat (including iron, choline, and an array of B vitamins), geese have a layer of fat under the skin that makes for an especially appetizing meal. Most American butchers these days remove the fat before selling the meat, but you should try to talk them into giving you the fat. Most of them just throw away the skins, so you can usually get a pretty good deal on it.
What To Do With It
Goose can be cooked like any bird: roasting, grilling, baking or frying. For a healthy dose of fat, be sure to leave the skin on. You can collect any fat that melts off while cooking and keep it for later. Use it to stir-fry vegetables or rub it over meat before throwing it in the oven the next time you bake or roast a nice, big hunk of flesh. It’ll make your meat crispy, tender, and delicious!
Mark Sisson touted the benefits of goose fat in his guide to animal fats.