Radio-frequency (RF) impairments, that exist inti- mately in wireless communications systems, can severely degrade the performance of traditional multiple-input multiple-output (MIMO) systems. Although compensation schemes can cancel out part of these RF impairments, there still remains a certain amount of impairments. These residual impairments have fun- damental impact on the MIMO system performance. However, most of the previous works have neglected this factor. In this paper, a training-based MIMO system with residual transmit RF impairments (RTRI) is considered. In particular, we derive a new channel estimator for the proposed model, and find that RTRI can create an irreducible estimation error floor. Moreover, we show that, in the presence of RTRI, the optimal training sequence length can be larger than the number of transmit antennas, especially in the low and high signal-to-noise ratio (SNR) regimes. An increase in the proposed approximated achievable rate is also observed by adopting the optimal training sequence length. When the training and data symbol powers are required to be equal, we demonstrate that, at high SNRs, systems with RTRI demand more training, whereas at low SNRs, such demands are nearly the same for all practical levels of RTRI.