It is well known that that chaff contaminates estimates of precipitation amounts. Hence it is important to remove (or censor) chaff in the field of radar reflectivity. Efficient and direct identification of chaff is possible with a polarimetric radar. By the end of this decade the US National Weather Service will introduce polarimetry to its WSR-88D network. Thus it is appropriate to examine polarimetric properties of chaff. We consider horizontal and vertical basis and covariances of corresponding returned signals. Because our prime objective is to identify chaff we concentrate on the co to cross polar correlation coefficient, the differential reflectivity and the linear depolarization ratio. We consider two models. In one, chaff is similar to prolate spheroids. Therefore, standard formulas could be applied to compute the elements of the covariance matrix. This approximation is applicable for chaff lengths much shorter than the wavelength (so that it is possible to compute the dipole moments). A more realistic approach is to model chaff as thin cylindrical antenna and apply standard formulas to obtain scattering coefficients. This second approach is also explored herein. Then, once the scattering coefficients are determined, the geometrical transformations, as done for the spheroids, can be used for computation of the polarimetric variables. For polarimetric variables that are independent of concentration and backscattering cross section, and chaff lengths up to and somewhat larger than half the wavelength, we show that the models produce equivalent results. In these computations chaff is assumed to have a uniform distribution of flutter angles (angle between the horizontal plane and chaff axis). We then report on some polarimetric signatures of chaff observed in the presence of precipitation. We end with few hypotheses that might explain these polarimetric measurements.