The Standard Model (SM) of particle physics fails to explain dark matter and why matter survived annihilation with antimatter following the Big Bang. Extensions to the SM, such as weak-scale Supersymmetry, may explain one or both of these phenomena by positing the existence of new particles and interactions that are asymmetric under time-reversal (T). These theories nearly always predict a small, yet potentially measurable (\(10^{-27}\)-\(10^{-30}\) \(e\) cm) electron electric dipole moment (EDM, \(d_e\)), which is an asymmetric charge distribution along the spin (\(\vec{S}\)). The EDM is also asymmetric under T. Using the polar molecule thorium monoxide (ThO), we measure \(d_e = (-2.1 \pm 3.7_\mathrm{stat} \pm 2.5_\mathrm{syst})\times 10^{-29}\) \(e\) cm. This corresponds to an upper limit of \(|d_e| < 8.7\times 10^{-29}\) \(e\) cm with 90 percent confidence, an order of magnitude improvement in sensitivity compared to the previous best limits. Our result constrains T-violating physics at the TeV energy scale.