  We point out the existence of a new general relativistic contribution to the
perihelion advance of Mercury that, while smaller than the contributions
arising from the solar quadrupole moment and angular momentum, is 100 times
larger than the second-post-Newtonian contribution. It arises in part from
relativistic "cross-terms" in the post-Newtonian equations of motion between
Mercury's interaction with the Sun and with the other planets, and in part from
an interaction between Mercury's motion and the gravitomagnetic field of the
moving planets. At a few parts in $10^6$ of the leading general relativistic
precession of 42.98 arcseconds per century, these effects are likely to be
detectable by the BepiColombo mission to place and track two orbiters around
Mercury, scheduled for launch around 2018.
