  A population protocol *stably elects a leader* if, for all $n$, starting from
an initial configuration with $n$ agents each in an identical state, with
probability 1 it reaches a configuration $\mathbf{y}$ that is correct (exactly
one agent is in a special leader state $\ell$) and stable (every configuration
reachable from $\mathbf{y}$ also has a single agent in state $\ell$). We show
that any population protocol that stably elects a leader requires $\Omega(n)$
expected "parallel time" --- $\Omega(n^2)$ expected total pairwise interactions
--- to reach such a stable configuration. Our result also informs the
understanding of the time complexity of chemical self-organization by showing
an essential difficulty in generating exact quantities of molecular species
quickly.
