Baking chicken in oven, but keeping it moist

The technique you describe is pretty much just the standard way of roasting a chicken. A V-shaped roasting rack is excellent for this purpose. As for keeping it moist, the standard technique is to brine the chicken first. Done properly, brining a chicken results in a moist, tender bird with crisp skin, and doesn't involve adding any additional fat. I normally brine by putting the chicken in a stew pot, covering it with cold water, adding about a cup of kosher salt, and letting it sit for 90 minutes.

If you're looking for moisture, your enemy is a combination of temperature and time -- if you cook it for too long (where too long depends on the temperature) the chicken is going to overcook and be dry.

Good methods are cooking it longer at a lower heat 'til it's cooked through, then giving it a burst of high heat to brown the skin. (there are also recipes done in reverse, where you pre-heat to a higher temp, then turn it down after a few minutes of cooking).

Brining can also help.

You'll get chicken fat when you eat the chicken no matter what method you use to roast it. To minimize how much fat you consume, don't eat the skin. You can also shred the chicken meat and dress it with some of the juices and fat.

I like the beer can method for keeping the chicken moist which someone else has already mentioned. Other methods include putting a pan of steaming hot water into the oven to keep the chicken company. Another is to cover the breast portion with foil for part of roasting time and make sur not to over roast.

Using the beer can chicken method is a way to keep a roasted chicken moist. Variations of this recipe abound. You can use just about any kind of can with just about any flavorful liquid.

Cover the bottom of the pan with sliced onions to keep the skin from sticking to the bottom.
Place chicken in pan UPSIDE DOWN (i.e. Breast down).
When there's about 20 minutes cooking time left (about 130 degrees F) 
flip it over, turn the heat up a bit and brown up the skin.

This way, all the juices flow into the breast, rather than out, and you end up with a very moist bird. I also like to pour lemon juice over the skin, and stuff the empty lemon half inside.

I put the whole chicken in a slow cooker with vegetables (but no extra liquid) and cook for 3-4 hours. I tried the beer can chicken once but didn't notice any difference from my normal roast chicken (maybe it was the beer!).

Stuffing the chicken with vegetables or fruits should help keep it moist as well as make it tasty.

As Joe said, the enemy of moist chicken is overcooking.

You can cook a chicken a shorter time at a higher temperature. For example, my favorite way of preparing pieces of chicken on the bone is from Barbara Kafka's cookbook Roasting. Heat the oven to 500 degrees (F). Season your chicken. Put it in the oven, skin side up, for 10 minutes. Flip, and cook another 10 minutes. Flip again and cook another 10 minutes. The chicken will be done at this point and quite juicy. You can even do this without the skin, and the chicken still comes out well.

Put 1kg (whole bag) of plain salt on the bottom of the roaster, put whole chicken on it, close the roaster lid and bake till the meat is done. The salt simply drains all dripping fat. The meat is delicious, the skin (in case you are eating it) is thin and crispy, all underskin fat is gone.

One thing people haven't mentioned though it was hinted at with Ray's post "your enemy is a combination of temperature and time".

The tip is this:

Use a smaller chicken if possible. Best would be a 3lb chicken cooked at very high heat (450+) for 45min or so. Make sure and let it rest for at least 10-15 minutes as well so that the juices have time to settle in the meat. Do not stuff it (unless its just tossing in some herbs or something small. You can also through some fresh herbs under the skin and just toss the skin when done since you are not eating it.

The small chickens are hard to find but it is possible at some stores like Trader Joes. Most large grocery stores tend to carry larger 5lb birds.

Just put in a more detailed answer here, but basically, try salting it for 20-30 minutes before you put it in the oven, and cook it until it's safe, but no longer. Use a probe thermometer to test it. Once it hits 160F, take it out, wrap it in foil, and let it sit for five to ten minutes to let the residual heat finish it off.