There exists an upper limit on the mass of black holes when the cosmol
ogical constant Lambda. is positive. We study the collision of two bla
ck holes whose total mass exceeds this limit, Our investigation is bas
ed on a recently discovered exact solution describing the collision of
Q=M black holes with Lambda>0. The global structure of this solution
is analyzed. We find that if the total mass is less than the extremal
limit, then the black holes coalesce. If it is greater, then a naked s
ingularity forms to the future of a Cauchy horizon. However, the horiz
on is not smooth. Generically, there is a mild curvature singularity,
which still allows geodesics to be extended. The implications of these
results for cosmic censorship are discussed.