The massively parallel halo finder MPI-Rockstar, based on the Rockstar (ascl:1210.008) phase-space temporal halo finder, is parallelized in a hybrid way using MPI and OpenMP, thus making it suitable for analysis on the hybrid shared and distributed memory environments of modern supercomputers. The implementation can analyze more than a trillion particles on more than 100,000 parallel processes. MPI-Rockstar also provides new functionality, which includes supporting HDF5 as an output format and output of additional halo properties such as the inertia tensor.