  We consider programmable matter that consists of computationally limited
devices (called particles) that are able to self-organize in order to achieve
some collective goal without the need for central control or external
intervention. We use the geometric amoebot model to describe such
self-organizing particle systems, which defines how particles can actively move
and communicate with one another. In this paper, we present an efficient
local-control algorithm which solves the leader election problem in O(n)
asynchronous rounds with high probability, where n is the number of particles
in the system. Our algorithm relies only on local information --- particles do
not have unique identifiers, any knowledge of n, or any sort of global
coordinate system --- and requires only constant memory per particle.
