  We propose solid-state gyroscopes based on ensembles of negatively charged
nitrogen-vacancy (${\rm NV^-}$) centers in diamond. In one scheme, rotation of
the nitrogen-vacancy symmetry axis will induce Berry phase shifts in the ${\rm
NV^{-}}$ electronic ground-state coherences proportional to the solid angle
subtended by the symmetry axis. We estimate sensitivity in the range of
$5\times10^{-3} {\rm rad/s/\sqrt{Hz}}$ in a 1 ${\rm mm^3}$ sensor volume using
a simple Ramsey sequence. Incorporating dynamical decoupling to suppress
dipolar relaxation may yield sensitivity at the level of $10^{-5} {\rm
rad/s/\sqrt{Hz}}$. With a modified Ramsey scheme, Berry phase shifts in the
${\rm ^{14}N}$ hyperfine sublevels would be employed. The projected sensitivity
is in the range of $10^{-5} {\rm rad/s/\sqrt{Hz}}$, however the smaller
gyromagnetic ratio reduces sensitivity to magnetic-field noise by several
orders of magnitude. Reaching $10^{-5} {\rm rad/s/\sqrt{Hz}}$ would represent
an order of magnitude improvement over other compact, solid-state gyroscope
technologies.
