  A ``bubble universe'' nucleating in an eternally inflating false vacuum will
experience, in the course of its expansion, collisions with an infinite number
of other bubbles. In an idealized model, we calculate the rate of collisions
around an observer inside a given reference bubble. We show that the collision
rate violates both the homogeneity and the isotropy of the bubble universe.
Each bubble has a center which can be related to ``the beginning of inflation''
in the parent false vacuum, and any observer not at the center will see an
anisotropic bubble collision rate that peaks in the outward direction.
Surprisingly, this memory of the onset of inflation persists no matter how much
time elapses before the nucleation of the reference bubble.
