This document describes the Brookhaven National Laboratory Proposal for the construction of a Relativistic Heavy Ion Collider (RHIC). The construction of this facility represents the natural continuation of the laboratory's role as a center for nuclear and high-energy physics research and extends and uses the existing AGS, Tandem Van de Graaff and CBA facilities at BNL in a very cost effective manner. The Administration and Congress have approved a project which will provide a link between the Tandem Van de Graaf and the AGS. Completion of this project in 1986 will provide fixed target capabilities at the AGS for heavy ions of about 14 GeV/amu with masses up to approx. 30 (sulfur). The addition of an AGS booster would extend the mass range to the heaviest ions (A approx. 200, e.g., gold); its construction could start in 1986 and be completed in three years. These two new AGS experimental facilities can be combined with the proposed Relativistic Heavy Ion Collider to extend the energy range to 100 x 100 GeV/amu for the heaviest ions. BNL proposes to start construction of RHIC in FY 86 with completion in FY 90 at a total cost of 134 M$.