Poisson's ratio in chiral Cosserat elastic solids is considered. Chirality allows the Poisson's ratio to exceed classical bounds, even if the material is directionally isotropic and all elastic moduli are within thermodynamic limits based on strain energy density. Poisson's ratio in chiral rods depends on the chiral elastic constants as well as on the shear and bulk moduli, assumed positive. Poisson's ratio can be greater than 0.5 or smaller than −1 for slender chiral specimens.