Space-time block coding (STBC) is a recent appealing solution to the problem of exploiting transmit diversity in multi-antenna systems for communications over flat fading channels. In a standard STBC scheme the receiver requires Channel State Information (CSI), which can be acquired via training at the expense of a reduced information rate. Alternatively, the requirement of CSI can be avoided altogether by using differential encoding. The existing trained or differential schemes for STBC assume that the channel is time-invariant during the transmission of at least two data blocks. However, wireless channels may be often time varying owing to frequency offsets induced by either Doppler shifts or carrier frequency mismatches. In this paper we present a simple trained STBC scheme for fading channels with frequency offsets.