We have implemented an experimental APL/C compiler, which accepts ordinary APL programs and produces C programs. We have also implemented a run-time environment that supports the parallel execution of these C programs on the RP3 computer, a shared-memory, 64-way MIMD machine built at the IBM Thomas J. Watson Research Center. The APL/C compiler uses the front end of the APL/370 compiler and imposes the same restrictions, but requires no parallelization directives from the user. The run-time environment is based on simple synchronization primitives and is implemented using Mach threads. We report the speedups of several compiled programs running on RP3 under the Mach operating system. The current implementation exploits only data parallelism. We discuss the relationship between the style of an APL program and its expected benefit from the automatic parallel execution provided by our compiler.