The Hopfield model for a neural network is studied in the limit when the number p of stored patterns increases with the size N of the network, as p=αN. It is shown that, despite its spin-glass features, the model exhibits associative memory for α<αc, αc≳0.14. This is a result of the existence at low temperature of 2p dynamically stable degenerate states, each of which is almost fully correlated with one of the patterns. These states become ground states at α<0.05. The phase diagram of this rich spin-glass is described.