  We study observed correlations between supermassive black hole (BHs) and the
properties of their host galaxies, and show that the observations define a BH
'fundamental plane' (BHFP), of the form M_BH sigma^(3.0+-0.3)*R_e^(0.43+-0.19),
or M_BH M_bulge^(0.54+-0.17)*sigma^(2.2+-0.5), analogous to the FP of
elliptical galaxies. The BHFP is preferred over a simple relation between M_BH
and any of sigma, M_bulge, M_dyn, or R_e alone at >99.9% significance. The
existence of this BHFP has important implications for the formation of
supermassive BHs and the masses of the very largest black holes, and
immediately resolves several apparent conflicts between the BH masses expected
and measured for outliers in both the M_BH-sigma and M_BH-M_bulge relations.
