The fabric itself may be a factor. I just handwashed my new Pearl Izumi baselayer undershirt and Garneau jersey after about five wearings (solo recreational rides only, no commutes, so no victim was subjected to odiferous abuse).

Before and after wearing I noticed a very slight chemical odor to the Garneau jersey -- not strong, reminiscent of that new car smell but much less noticeable. It seems to be coming from the elastic in the waistband and rear pockets. The Garneau jersey uses quite a bit more elastic than I'd have expected -- it feels like 1/2" wide strips of thick rubbery material, more like a bungee cord than most clothing type elastic. I suppose anyone who's particularly sensitive could choose jerseys with zipper rear pockets and no elastic waistband.

The Pearl Izumi was odorless as far as I could tell. After a few rides the Pearl Izumi undershirt still had very low odor -- I'll definitely be getting another for summer wear under my casual shirts for leisurely jaunts downtown. The Garneau jersey had a bit of body odor after wearing, but not nearly as bad as my cotton shirts.

After handwashing and air drying, the Pearl Izumi was odorless again. But the Garneau jersey still has the very slight manufacturing chemical sort of odor. It's so slight I can't smell it at all if I have any nasal allergy symptoms -- only when my sinuses are completely clear can I detect a slight odor.

Maybe there's a good reason Pearl Izumi stuff is so much more expensive than some makers. I suppose I'd consider that in choosing bike clothing for commuting or casual social rides.