There are a lot of interesting chemistry and biochemistry issues involved in this. My favorite, and one I'm surprised no one has mentioned yet, is the chirality of the amino acids, and other complicated organics, in living things.
Much of the chirality problem can be explained stochastically®. If the chirality of the "offspring" (biological, crystal, etc.) is the same as that of the parents, luck will select one type only.
Computer Experiment (I've actually run this several times):
I. Start with some population (balanced, unbalanced, I used 100 right and 100 left handed entities.)
II. Allow each entity to reproduce (deterministically is easy, I just doubled the number of each.)
III. For each entity, kill with some probablity (I used 1/2 to correspond with II.)
IV. If both species present, go to II.
This runs fast, (no storage.) It's the same mathematically as matching pennies; whoever is ahead stays ahead, ties are rare.