Niobium (Nb) Superconducting RF (SRF) cavities have been used or will be used for a number of particle accelerators. The fundamental limit of the accelerating gradient has been thought to be around 50 MV/m due to its RF critical magnetic field of around 200 mT. This limit will prevent new projects requiring higher gradient and compact accelerators from considering SRF structures. There is a theory, however, that promises to overcome this limitation by coating thin (less than the penetration depth) superconductors on Nb. We initiated measurements of critical magnetic fields of Nb coated with various thin film superconductors, starting with MgB2 films deposited using reactive evaporation technique, with the goal to apply this coating to SRF cavities. This paper will present first test results of the RF critical magnetic field of a system consisting of a 10 nm B and a 100 nm MgB2 films deposited on a chemically polished 2-inch single grain Nb substrate.