Coexistence of competitive species is severely limited by the availability of resources and the characteristics of the environment. In particular, the so-called 'competitive exclusion principle' states that, at equilibrium, the number of coexisting species cannot be larger than the number of resources for which they compete. However, many in situ observations have revealed prolonged coexistence of a large number of competitive plankton species, a phenomenon known as 'the paradox of the plankton'. Here we investigate this problem and show that ocean mesoscale vortices generate transport barriers and incomplete horizontal mixing, allowing for a prolonged survival of the less-fit species, even for fully homogeneous resource distributions. In such a situation, the temporarily less-fit plankton species are protected from competition by the action of the vortices.