Inflation ends with the formation of a Bose condensate of inflatons. We show that in hybrid inflation models this condensate is typically unstable with respect to spatial perturbations and can fragment to condensate lumps. The case of D-term inflation is considered as an example and it is shown that fragmentation occurs if λ≳0.2g, where λ is the superpotential coupling and g is the U(1)FI gauge coupling. Condensate fragmentation can result in an effective enhancement of inflaton annihilations over decays as the main mode of reheating. In the case of D-term inflation models in which the standard model fields carry U(1)FI charges, if condensate fragmentation occurs then reheating is dominated by inflaton annihilations, typically resulting in the overproduction of thermal gravitinos. Fragmentation may also have important consequences for SUSY flat direction dynamics and for preheating.