The 15O(alpha,gamma)19Ne reaction is one of two routes for breakout from the hot CNO cycles into the rp process in accreting neutron stars. Its astrophysical rate depends critically on the decay properties of excited states in 19Ne lying just above the 15O + alpha threshold. We have measured the alpha-decay branching ratios for these states using the p(21Ne,t)19Ne reaction at 43 MeV/u. Combining our measurements with previous determinations of the radiative widths of these states, we conclude that no significant breakout from the hot CNO cycle into the rp process in novae is possible via 15O(alpha,gamma)19Ne, assuming current models accurately represent their temperature and density conditions.