Time-resolved X-ray spectroscopy has been obtained for the narrow line Seyfert galaxy Mrk 766 from XMM-Newton observations . We present analysis in the energy-time plane of EPIC pn data in the 4 - 8 keV band with energy resolution R \simeq 50 . A component of Fe K \alpha emission detected in the maps shows a variation of photon energy with time that appears both to be statistically significant and to be consistent with sinusoidal variation . We investigate the interpretation that there exists a component of line emission from matter in a Keplerian orbit around a supermassive black hole . The orbit has a period \sim 165 ks and a line-of-sight velocity \sim 13 , 500 km s ^ { -1 } . This yields a lower limit for the central mass of M > 4.9 \times 10 ^ { 5 } { M } _ { \odot } within a radius of 3.6 \times 10 ^ { 13 } cm ( 2.4 A.U . ) . The orbit parameters are consistent with higher black hole masses , but the lack of any substantial gravitational redshift of the orbit implies an upper limit to the black hole mass of 4.5 \times 10 ^ { 7 } M _ { \odot } .