  In this work, we introduce GRChombo: a new numerical relativity code which
incorporates full adaptive mesh refinement (AMR) using block structured
Berger-Rigoutsos grid generation. The code supports non-trivial
"many-boxes-in-many-boxes" mesh hierarchies and massive parallelism through the
Message Passing Interface (MPI). GRChombo evolves the Einstein equation using
the standard BSSN formalism, with an option to turn on CCZ4 constraint damping
if required. The AMR capability permits the study of a range of new physics
which has previously been computationally infeasible in a full 3+1 setting,
whilst also significantly simplifying the process of setting up the mesh for
these problems. We show that GRChombo can stably and accurately evolve standard
spacetimes such as binary black hole mergers and scalar collapses into black
holes, demonstrate the performance characteristics of our code, and discuss
various physics problems which stand to benefit from the AMR technique.
