There are naturally occurring organic compounds which may have only right or left optical handedness ...

My information is that each of the amino acids (except the simplest one) exists in two such forms, and that when multiple amino acid chain together to form a protein, the links the acids stable only if all the acids are the same form -- one or the other. As a result, life -- on earth, anyway -- uses only one form, which is the one we happen to call the L-form.
PS: In those few meteorites in which amino acids have been found, they are split roughly 50-50 between the two form. At least as of my the date of my source, from the 1970's.

But does this have anything to do with why most people are either right- or left-handed, or why the righthandedness is far more common?