  By extending the Poisson algebra of ideal hydrodynamics to include a
two-index tensor field, we construct a new (2+1)-dimensional hydrodynamic
theory that we call "chiral metric hydrodynamics." The theory breaks spatial
parity and contains a degree of freedom which can be interpreted as a dynamical
metric, and describes a medium which behaves like a solid at high frequency and
a fluid with odd viscosity at low frequency. We derive a version of the Kelvin
circulation theorem for the new hydrodynamics, in which the vorticity is
replaced by a linear combination of the vorticity and the dynamical Gaussian
curvature density. We argue that the chiral metric hydrodynamics, coupled to a
dynamical gauge field, correctly describes the long-wavelength dynamics of
quantum Hall Jain states with filling factors $\nu=N/(2N+1)$ and
$\nu=(N+1)/(2N+1)$ at large $N$. The Kelvin circulation theorem implies a
relationship between the electron density and the dynamical Gaussian curvature
density. We present an purely algebraic derivation of the low-momentum
asymptotics of the static structure factor of the Jain states.
