We study relativistic hydrodynamics of normal fluids in two spatial dimensions. When the microscopic theory breaks parity, extra transport coefficients appear in the hydrodynamic regime, including the Hall viscosity and the anomalous Hall conductivity. I present a classification of all these transport coefficients in first order hydrodynamics. All the parity-breaking transport coefficients turn out to be dissipationless, and some of them are related to the thermodynamic response to an external magnetic field and to vorticity. The latter ones are parametrized in terms of a ordinary and a vortical magnetization, plus one more integration constant, which is a function of temperature. For a large class of systems for which Euclidean correlators can be obtained from a generating functional, this integration constant will vanish. Finally, I give a holographic example of a strongly interacting relativistic fluid where the new parity-violating transport coefficients are computable.