Chop the onion into rings and put them into the bottom of a dutch oven or Le Cruset pot.
Pull out the giblet bag from inside the chicken and rinse chicken off. Toss it into the pot.
Chop up the shallots (except for 1), carrots and potatoes and insert them into the cavity of the chicken.
There is some fat that most people generally clean off and discard on the skin surrounding the chicken cavity. Pull this fat off and put it into a small iron skillet (DO NOT DO THIS WITH NON-STICK, it will ruin your non-stick). Heat the chicken fat. As the fat heats and melts, finely chop the last shallot, and throw it and the up paprika into the chicken fat. Sautee the onions and paprika until the onions turn translucent, spoon the mixture over the chicken, using the still-bubbling fat remainder bits to rub the paprika all over the chickens skin. Discard the remaining fat bits.
Put the lid on, and pop it into the oven.
Cook at 350 for 40 minutes, checking every 20 minutes, turn the oven up to 400 for 10-20 minutes, take the lid off and crank the heat to 450 for the last 10-15 minutes.