  We consider exclusion processes on a rooted $d$-regular tree. We start from a
Bernoulli product measure conditioned on having a particle at the root, which
we call the tagged particle. For $d\geq 3$, we show that the tagged particle
has positive linear speed and satisfies a central limit theorem. We give an
explicit formula for the speed. As a key step in the proof, we first show that
the exclusion process "seen from the tagged particle" has an ergodic invariant
measure.
