Apart from subtle violations of CP symmetry by the weak interactions, the basic laws of physics are time-reversal invariant. Nevertheless, in the macroscopic world, time has a very definite direction, or arrow. Given that the dynamics of a closed system are time-reversal invariant, the arrow of time is introduced through boundary or initial conditions. In this Letter it is argued that if the Hamiltonian for a system, H, has the property THT(-1)=-H for a unitary transformation T, then the system can, in principle, be made to evolve backward in time. The prototype of this sort of behavior is the spin echo. Calculations for a single-band tight-binding model suggest that it may be possible to observe the electronic counterpart, or charge echo.