  It is widely believed that special initial conditions must be imposed on any
time-symmetric law if its solutions are to exhibit behavior of any kind that
defines an `arrow of time'. We show that this is not so. The simplest
non-trivial time-symmetric law that can be used to model a dynamically closed
universe is the Newtonian $N$-body problem with vanishing total energy and
angular momentum. Because of special properties of this system (likely to be
shared by any law of the Universe), its typical solutions all divide at a
uniquely defined point into two halves. In each a well-defined measure of shape
complexity fluctuates but grows irreversibly between rising bounds from that
point. Structures that store dynamical information are created as the
complexity grows and act as `records'. Each solution can be viewed as having a
single past and two distinct futures emerging from it. Any internal observer
must be in one half of the solution and will only be aware of the records of
one branch and deduce a unique past and future direction from inspection of the
available records.
