  The decay $b\to d e^+e^-$ has an amplitude containing comparable
contributions proportional to $V_{tb}V_{td}^{*}$, $V_{cb}V_{cd}^{*}$ and
$V_{ub}V_{ud}^{*}$. These pieces involve different unitarity phases produced by
$c\bar{c}$ and $u\bar{u}$ loops. The simultaneous presence of different CKM
phases and different dynamical phases leads to a calculable asymmetry in the
partial widths of $b\to d e^+e^-$ and $\bar{b}\to \bar{d} e^+e^-$. Using the
effective Hamiltonian of the standard model, we calculate this asymmetry as a
function of the $e^+e^-$ invariant mass. The effects of $\rho$, $\omega$ and
$J/\psi$ resonances are taken into account in the vacuum polarization of the
$u\bar{u}$ and $c\bar{c}$ currents. As a typical result, an asymmetry of $- 5%
(- 2%)$ is predicted in the nonresonant domain $1 GeV < m_{e^+e^-} <
m_{J/\psi}$, assuming $\eta = 0.34$ and $\rho= 0.3 (-0.3)$. The branching ratio
in this domain is $1.2\times 10^{-7} (3.3\times 10^{-7})$. Results are also
obtained in the region of the $J/\psi$ resonance, where an asymmetry of
$3\times 10^{-3}$ is expected, subject to certain theoretical uncertainties in
the $b\to d J/\psi$ amplitude.
