  We present first results for $B_c$ spectroscopy using Lattice
Non-Relativistic QCD (NRQCD). For the NRQCD action the leading order
spin-dependent and next to leading order spin-independent interactions have
been included with tadpole-improved coefficients. We use multi-exponential fits
to multiple correlation functions to extract ground and excited $S$ states and
give accurate values for the $S$ state hyperfine splitting and the P state
($B^{**}_c$) fine structure, including the effects of $^1P_1/^3P_1$ mixing.
