  The millisecond pulsar PSR B1620-26, in the globular cluster M4, has a white
dwarf companion in a half-year orbit. Anomalously large variations in the
pulsar's apparent spin-down rate have suggested the presence of a second
companion in a much wider orbit. Using timing observations made on more than
seven hundred days spanning eleven years, we confirm this anomalous timing
behavior. We explicitly demonstrate, for the first time, that a timing model
consisting of the sum of two non-interacting Keplerian orbits can account for
the observed signal. Both circular and elliptical orbits are allowed, although
highly eccentric orbits require improbable orbital geometries.
  The motion of the pulsar in the inner orbit is very nearly a Keplerian
ellipse, but the tidal effects of the outer companion cause variations in the
orbital elements. We have measured the change in the projected semi-major axis
of the orbit, which is dominated by precession-driven changes in the orbital
inclination. This measurement, along with limits on the rate of change of other
orbital elements, can be used to significantly restrict the properties of the
outer orbit. We find that the second companion most likely has a mass m~0.01
Msun --- it is almost certainly below the hydrogen burning limit (m<0.036 Msun,
95% confidence) --- and has a current distance from the binary of ~35 AU and
orbital period of order one hundred years. Circular (and near-circular) orbits
are allowed only if the pulsar magnetic field is ~3x10^9 G, an order of
magnitude higher than a typical millisecond pulsar field strength. In this
case, the companion has mass m~1.2x10^-3 Msun and orbital period ~62 years.
