  Nearly 150 massive black hole binary (MBHB) candidates at sub-pc orbital
separations have been reported in recent literature. Nevertheless, the
definitive detection of even a single such object remains elusive. If at least
one of the black holes is accreting, the light emitted from its accretion disc
will be lensed by the other black hole for binary orbital inclinations near to
the line of sight. This binary self-lensing could provide a unique signature of
compact MBHB systems. We show that, for MBHBs with masses in the range 10^6 -
10^10 solar masses and with orbital periods less than ~10 yr, strong lensing
events should occur in one to 10s of percent of MBHB systems that are monitored
for an entire orbit. Lensing events will last from days for the less massive,
shorter period MBHBs up to a year for the most massive ~10 year orbital period
MBHBs. At small inclinations of the binary orbit to the line of sight, lensing
must occur and will be accompanied by periodicity due to the relativistic
Doppler boost. Flares at the same phase as the otherwise average flux of the
Doppler modulation would be a smoking gun signature of self-lensing and can be
used to constrain binary parameters. For MBHBs with separation >100
Schwarzschild radii, we show that finite-sized source effects could serve as a
probe of MBH accretion disc structure. Finally, we stress that our lensing
probability estimate implies that ~10 of the known MBHB candidates identified
through quasar periodicity should exhibit strong lensing flares.
