With an instantaneous view of 70% of the sky, the Fermi Gamma-ray Burst Monitor (GBM) is an excellent partner in the search for electromagnetic counterparts to gravitational wave (GW) events. GBM observations at the time of the Laser Interferometer Gravitational-wave Observatory (LIGO) event GW150914 reveal the presence of a weak transient above 50 keV, 0.4~s after the GW event, with a false alarm probability of 0.0022 (2.9$σ$). This weak transient lasting 1 s was not detected by any other instrument and does not appear connected with other previously known astrophysical, solar, terrestrial, or magnetospheric activity. Its localization is ill-constrained but consistent with the direction of GW150914. The duration and spectrum of the transient event are consistent with a weak short Gamma-Ray Burst arriving at a large angle to the direction in which Fermi was pointing, where the GBM detector response is not optimal. If the GBM transient is associated with GW150914, this electromagnetic signal from a stellar mass black hole binary merger is unexpected. We calculate a luminosity in hard X-ray emission between 1~keV and 10~MeV of $1.8^{+1.5}_{-1.0} \times 10^{49}$~erg~s$^{-1}$. Future joint observations of GW events by LIGO/Virgo and Fermi GBM could reveal whether the weak transient reported here is a plausible counterpart to GW150914 or a chance coincidence, and will further probe the connection between compact binary mergers and short Gamma-Ray Bursts. ; Comment: Accepted for publication in ApJL