  The Gaia mission recently revealed an excess population of equal-mass "twin"
wide binaries, with mass ratio $q\gtrsim 0.95$, extending to separations of at
least 1000 AU. The origin of this population is an enigma: twin binaries are
thought to form via correlated accretion in circumbinary disks, but the typical
observed protostellar disks have radii of $\sim100$ AU, far smaller than the
separations of the widest twins. Here, we infer the eccentricity distribution
of wide twins from the distribution of their $v$-$r$ angles, i.e., the angle
between the components' separation and relative velocity vectors. We find that
wide twins must be on extremely eccentric orbits. For the excess-twin
population at 400-1000 AU, we infer a near-delta function excess of
high-eccentricity system, with eccentricity $0.95 \lesssim e \leq 1$. These
high eccentricities for wide twins imply pericenter distances of order $10$ AU
and suggest that their orbits were scattered via dynamical interactions in
their birth environments, consistent with a scenario in which twins are born in
circumbinary disks and subsequently widened. These results further establish
twin wide binaries as a distinct population and imply that wide twins can be
used as a probe of the dynamical history of stellar populations.
