I'm also a polymer guy and have little physics understanding, but I may be able to shed a little light on the subject <pun intended>. It looks like most of the answer is here in the posts above with just a little clarification needed. First, here's a couple of good links I used to help me brush up on the subject. I use polarizers in a microscope all the time so I guess it would be nice to know how they work.
http://en.wikipedia.org/wiki/Polarizer
http://www.olympusmicro.com/pr...olor/polarization.html
For a light wave to be absorbed by a molecule, it must be in a specific orientation relative to the molecule. For instance in infrared absorption spectroscopy, the light must be oriented parallel to the bond to be absorbed by the bond and add to its vibrational energy. I'm sure there are many different ways molecules can absorb light depending on the wavelength in question, but most will require orientation with something in the molecule. In fact infrared spectroscopy takes advantage of this in a technique known as dichroism to determine the alignment (or lack thereof) in molecules.
So with this piece of information, the first thing I would like to clear up is that the material in polarizers is never a "chaotic array of molecules". In science, this would be referred to as isotropic, meaning that the property in question is not dependent on angle, or the same in all directions. The fact that polaizers can polarize light directly evidences the fact that they are anisotropic, not the same in all directions. The olympus link above gives some ideas about how this is done. It can be as simple as stretching plastic in the melt state before cooling so that the polymer chains are aligned in one direction, or sometimes non-spherical nanofillers are added that also align during stretching.
As for chiral molecules, they will rotate the orientation of light, but can only polarize it if the bulk material somehow orients itself so that absorption is occuring preferentially in one direction. But, polarizers are very useful for viewing oriented molecules because of the fact that they rotate light. This is the underlying concept of polarized optical microscopy that allows me to view crystals, liquid crystals, and stress birefringence. Essentially, a polarizer polarizes incoming light before it meets the sample. Then, if the sample can rotate light (most organics) and can do so preferentially in one direction (generally requires and ordered structure) then after the light passes through the sample and meets another polarizer oriented at 90 degrees to the first, only light that has been rotated can pass through. This makes for very beautiful pictures of lighted crystals on a black background.
Hope this helps.
-Tim