We consider the problem of channel estimation in a multiple-input-multiple-output (MIMO) full-duplex (FD) wireless communication system assisted by a reconfigurable intelligent surface (RIS) with hardware impairments (HI) occurring at the transceivers and RIS elements. We propose an unbiased channel estimator that requires knowledge of only the first and second order statistics of the HI, for which we derive closed form expressions. The proposed estimator reduces to the maximum likelihood estimator (MLE) in the case of ideal hardware. We also describe FD and HD orthogonal pilot schemes that minimize the mean square error of the MLE in the case of ideal hardware. We verify the performance of the estimator under varying conditions of transceiver and RIS HI via numerical simulations.