A classic result of Chvatál and Erdős (1972) asserts that, if the vertex-connectivity of a graph G is at least as large as its independence number, then G has a Hamilton cycle. We prove a similar result, implying that a graph G is pancyclic, namely it contains cycles of all lengths between 3 and |G|: we show that if |G| is large and the vertex-connectivity of G is larger than its independence number, then G is pancyclic. This confirms a conjecture of Jackson and Ordaz (1990) for large graphs.