Rateless codes are good codes of infinite length that have the property that prefixes of such codes are themselves good codes. This makes them attractive for applications in which the channel quality is uncertain, where systems transmit as much of a codeword as necessary for decoding to be possible. In particular, rateless codes are potentially attractive for wireless communication. In a recent work, a rateless coding scheme was proposed for the AWGN channel, based on layering, repetition and random dithering. We extend this scheme to multiple-input single-output (MISO) Gaussian channels. We show that the rate loss associated with orthogonal design space-time codes may be alleviated by layering and dithering, very similar to the rateless approach for the AWGN channel. We then combine the two schemes and arrive at a close-to-capacity rateless code for MISO channels. The required complexity depends on the fraction of capacity that is targeted, is linear in the capacity of the channel and does not depend on the number of transmit antennas. Furthermore, the coding scheme uses only one base AWGN code