Vacuum packed chicken with air bubbles

Normally, a couple of days (1-2) past sell-by date doesn't mean you must throw it away; companies build in a couple of days past the sell-by date when determining their product dating. However, once at this point, it should be immediately cooked.
Keeping that in mind, the following are extremely important:
1. Poultry must always be cooked to a minimum internal temperature of 165F. There is some discussion on cooking it to higher temps of 175-185, depending on the source. Cooking to this temperature ensures any harmful bacteria is killed. Ensure you wash your hands thoroughly after handling uncooked poultry to avoid cross-contamination.
2. When looking at vacuum packed fresh meats in the store, always avoid packages that are loose, as this indicates the possible presence of pinholes or breaches in the packaging, which negatively impact the sell-by date, as they allow bacteria to infiltrate the packaging. Tightly sealed packing is best.
3. If the package was tightly sealed when purchased, and now shows bubbles and bulging, this indicates the likely presence of bacteria in the meat - this package may have been mishandled causing a pinhole somewhere along the way, or may have had a breach in the cold chain (i.e. it was in a cart for an hour and then placed back into the fridge.) If there is potential that it was mishandled, I wouldn't recommend consuming it.
(Keep in mind as well that this is only for vacuum packed meats - some meats are gas-flushed, and are therefore loose in the package - although this is not typically done in the fresh poultry industry.)

Agree with Pegeen. I've even thrown out chicken a day or two before the sell by date b/c it smelled a little funky when I opened it. Since then I try to cook chicken well within the period between purchase and sell by date. If I can't I freeze it.

Someone else may be able to provide an explanation for whether it's an unhealthy bacteria that's causing the plastic to bulge. But to give you a quick answer, I would not use a chicken past its sell-by date. Throw it out, don't use it. When I have a chicken or chicken parts nearing the sell-by, if I know I'm not going to use it soon, I double-wrap it and freeze it before the sell-by.