  Recently, we have extended the X-ray reflection model relxill to test the
spacetime metric in the strong gravitational field of astrophysical black
holes. In the present Letter, we employ this extended model to analyze
XMM-Newton, NuSTAR, and Swift data of the supermassive black hole in 1H0707-495
and test deviations from a Kerr metric parametrized by the Johannsen
deformation parameter $\alpha_{13}$. Our results are consistent with the
hypothesis that the spacetime metric around the black hole in 1H0707-495 is
described by the Kerr solution.
