Although CP violation in the B meson system has been well established by the B factories, there has been no direct observation of time reversal violation. The decays of entangled neutral B mesons into definite flavor states ($B^0$ or $\bar{B}^0$), and $J/\psi K_S^0$ or $c\bar{c} K_S^0$ final states (referred to as $B_+$ or $B_-$), allow comparisons between the probabilities of four pairs of T-conjugated transitions, for example, $\bar{B}^0 \rightarrow B_-$ and $B_- \rightarrow \bar{B}^0$, as a function of the time difference between the two B decays. Using 468 million $B\bar{B}$ pairs produced in $\Upsilon(4S)$ decays collected by the BABAR detector at SLAC, we measure T-violating parameters in the time evolution of neutral B mesons, yielding $\Delta S_T^+ = -1.37 \pm 0.14 (stat.) \pm 0.06 (syst.)$ and $\Delta S_T^- = 1.17 \pm 0.18 (stat.) \pm 0.11 (syst.)$. These nonzero results represent the first direct observation of T violation through the exchange of initial and final states in transitions that can only be connected by a T-symmetry transformation. Show Partial Abstract