  Massive Dirac particles are a superposition of left and right chiral
components. Since chirality is not a conserved quantity, the free Dirac
Hamiltonian evolution induces chiral quantum oscillations, a phenomenon related
to the \textit{Zitterbewegung}, the trembling motion of free propagating
particles. While not observable for particles in relativistic dynamical
regimes, chiral oscillations become relevant when the particle's rest energy is
comparable to its momentum. In this paper, we quantify the effect of chiral
oscillations on the non-relativistic evolution of a particle state described as
a Dirac bispinor and specialize our results to describe the interplay between
chiral and flavor oscillations of non-relativistic neutrinos: we compute the
time-averaged survival probability and observe an energy-dependent depletion of
the quantity when compared to the standard oscillation formula. In the
non-relativistic regime, this depletion due to chiral oscillations can be as
large as 40$\%$. Finally, we discuss the relevance of chiral oscillations in
upcoming experiments which will probe the cosmic neutrino background.
