We describe the design and current status of a new X-ray cluster survey aimed at the compilation of a statistically complete sample of very X-ray luminous (and thus, by inference, massive), distant clusters of galaxies. The primary goal of the MAssive Cluster Survey (MACS) is to increase the number of known massive clusters at z>0.3 from a handful to hundreds. Upon completion of the survey, the MACS cluster sample will greatly improve our ability to study quantitatively the physical and cosmological parameters driving cluster evolution at redshifts and luminosities poorly sampled by all existing surveys. To achieve these goals we apply an X-ray flux and X-ray hardness-ratio cut to select distant cluster candidates from the ROSAT Bright Source Catalogue. Starting from a list of more than 5,000 X-ray sources within the survey area of 22,735 square degrees we use positional cross-correlations with public catalogues of Galactic and extragalactic objects, reference to APM colours, visual inspection of Digitized Sky Survey images, extensive CCD imaging, and finally spectroscopic observations with the University of Hawaiis 2.2m and the Keck 10m telescopes to compile the final cluster sample. We discuss in detail the X-ray selection procedure and the resulting selection function, and present model predictions for the number of distant clusters expected to emerge from MACS. At the time of this writing the MACS cluster sample comprises 101 spectroscopically confirmed clusters at 0.3<z<0.6; more than two thirds of these are new discoveries. Our preliminary sample is already 15 times larger than that of the EMSS in the same redshift and X-ray luminosity range.