  We consider a branching Brownian motion in which binary fission takes place
only when particles are at the origin at a rate \beta > 0 on the local time
scale. We obtain results regarding the asymptotic behaviour of the number of
particles above \lambda t at time t, for \lambda > 0. As a corollary, we
establish the almost sure asymptotic speed of the rightmost particle. We also
prove a Strong Law of Large Numbers for this catalytic branching Brownian
motion.
