The spin-orbit induced predissociation dynamics of the A(2)Sigma (+)(nu ;N) rovibronic states of HCl+ has been investigated by numerical solution of four coupled time-dependent Schrodinger equations based on ab initio data. The rotational dependence of the predissociation lifetime exhibits pronounced peaks with lifetimes up to one order of magnitude larger than that of neighboring levels. The origin and possible applications of these 'rotational islands of stability' are discussed.