We are developing a system for collaborative research and development for a distributed group of researchers at different institutions around the world. In a new paradigm for {collaborative} computational science, the computer code and supporting infrastructure itself becomes the collaborating instrument, just as an accelerator becomes the collaborating tool for large numbers of distributed researchers in particle physics. The design of this ``Collaboratory'' allows many users, with very different areas of expertise, to work coherently together, on distributed computers around world. Different supercomputers may be used separately, or for problems exceeding the capacity of any single system, multiple supercomputers may be networked together through high speed gigabit networks. Central to this Collaboratory is a new type of community simulation code, called ``Cactus''. The scientific driving force behind this project is the simulation of Einstein's equations for studying black holes, gravitational waves, and neutron stars, which has brought together researchers in very different fields from many groups around the world to make advances in the study of relativity and astrophysics. But the system is also being developed to provide scientists and engineers, without expert knowledge of parallel or distributed computing, mesh refinement, and so on, with a simple framework for solving any system of partial differential equations on many parallel computer systems, from traditional supercomputers to networks of workstations.