Early Release Science observations of the cluster NGC 3603 with the WFC3 on the refurbished Hubble Space Telescope allow us to study its recent star formation history. Our analysis focuses on stars with Hα excess emission, a robust indicator of their pre-main sequence (PMS) accreting status. The comparison with theoretical PMS isochrones shows that 2/3 of the objects with Hα excess emission have ages from 1 to 10 Myr, with a median value of 3 Myr, while a surprising 1/3 of them are older than 10 Myr. The study of the spatial distribution of these PMS stars allows us to confirm their cluster membership and to statistically separate them from field stars. This result establishes unambiguously for the first time that star formation in and around the cluster has been ongoing for at least 10-20 Myr, at an apparently increasing rate.