  The distribution of a Markov process with killing, conditioned to be still
alive at a given time, can be approximated by a Fleming-Viot type particle
system. In such a system, each particle is simulated independently according to
the law of the underlying Markov process, and branches onto another particle at
each killing time. The consistency of this method in the large population limit
was the subject of several recent articles. In the present paper, we go one
step forward and prove a central limit theorem for the law of the Fleming-Viot
particle system at a given time under two conditions: a "soft killing"
assumption and a boundedness condition involving the "carr\'e du champ"
operator of the underlying Markov process.
