  The direction of the orbital angular momentum of the $B$-phase of superfluid
$^3$He can be controlled by engineering the anisotropy of the silica aerogel
framework within which it is imbibed. In this work, we report our discovery of
an unusual and abrupt `orbital-flop' transition of the superfluid angular
momentum between orientations perpendicular and parallel to the anisotropy
axis. The transition has no hysteresis, warming or cooling, as expected for a
continuous thermodynamic transition, and is not the result of a competition
between strain and magnetic field. This demonstrates the spontaneous
reorientation of the order parameter of an unconventional BCS condensate.
