We present a parallel implementation of a map-making algorithm for CMB anisotropy experiments which is both fast and efficient. We show for the first time a Maximum Likelihood, minimum variance map obtained by processing the entire data stream expected from the Planck Surveyor, under the assumption of a symmetric beam profile. Here we restrict ourselves to the case of the 30 GHz channel of the Planck Low Frequency Instrument. The extension to Planck higher frequency channels is straightforward. If the satellite pointing periodicity is good enough to average data that belong to the same sky circle, then the code runs very efficiently on workstations. The serial version of our code also runs on very competitive time-scales the map-making pipeline for current and forthcoming balloon borne experiments.