  We prove that the C*-algebra of a second-countable, \'etale, amenable
groupoid is simple if and only if the groupoid is topologically principal and
minimal. We also show that if G has totally disconnected unit space, then the
associated complex *-algebra introduced by Steinberg is simple if and only if
the interior of the isotropy subgroupoid of G is equal to the unit space and G
is minimal.
