  The decoherence of a two-state tunneling molecule, such as a chiral molecule
or ammonia, due to collisions with a buffer gas is analyzed in terms of a
succession of quantum states of the molecule satisfying the conditions for a
consistent family of histories. With $\hbar \omega$ the separation in energy of
the levels in the isolated molecule and $\gamma$ a decoherence rate
proportional to the rate of collisions, we find for $\gamma \gg \omega$ (strong
decoherence) a consistent family in which the molecule flips randomly back and
forth between the left- and right-handed chiral states in a stationary Markov
process. For $\gamma < \omega$ there is a family in which the molecule
oscillates continuously between the different chiral states, but with
occasional random changes of phase, at a frequency that goes to zero at a phase
transition $\gamma = \omega$. This transition is similar to the behavior of the
inversion frequency of ammonia with increasing pressure, but will be difficult
to observe in chiral molecules such as D$_2$S$_2$. There are additional
consistent families both for $\gamma > \omega$ and for $\gamma < \omega$. In
addition we relate the speed with which chiral information is transferred to
the environment to the rate of decrease of complementary types of information
(e.g., parity information) remaining in the molecule itself.
