The electric dipole moment of the ground state of cesium, d$\sb{\rm Cs}$, is measured. This result is related to the electric dipole moment of the electron in a straightforward way using the results of atomic theory calculations found in the literature. The resulting limit of the electric dipole moment of the electron represents a stringent test of time reversal invariance. Cesium vapor is studied at zero magnetic field in glass cells which also contain 250 torr of nitrogen. The ground state of cesium is optically pumped by a laser beam and the atomic orientation undergoes the electrical analog of Larmor precession due to an applied electric field. The precession is detected by comparing the transmission rates of left and right circularly polarized light for a second laser beam which is orthogonal to both the initial laser beam and the applied electric field. The Hamiltonians H = $\vec\mu\cdot\vec B$ and H = $\vec d\cdot\vec E$ are interchangeable allowing calibration of the apparatus using an applied magnetic field. During data acquisition all three components of the effective magnetic field are reduced below 100 nG. Comparing signals from two cells with opposite electric fields eliminates signals due to drifts in the homogeneous magnetic field. Comparing the signals from four cells, two with electric fields and two without, reduces noise due to fluctuating magnetic fields to about 150 pG in 20 seconds of integration (a single data point.) The precession frequency is determined with a statistical precision of 0.5 $\mu$Hz in a two day data collection run. A set of 13 data runs, 9 in the two cell configuration and 4 in the four cell configuration, is used to place upper limits d$\sb{\rm Cs}$ $<$ 1.1 $\times$ 10$\sp{-24}$e-cm, d$\sb{\rm e}$ $<$ 9.3 $\times$ 10$\sp{-27}$e-cm and a limit on T-violating electron-nucleon scaler interactions of C$\sb{\rm S}$ $<$ 10$\sp{-5}\rm G\sb{\rm F}$. This limit represents an order of magnitude improvement over the previously limits on d$\sb{\rm Cs}$ and constrains theories attempting to explain the violation of CP invariance which is seen in the K meson system.