  The rich SMC star cluster NGC419 has recently been found to present both a
broad main sequence turn-off and a dual red clump of giants, in the sharp
colour-magnitude diagrams (CMD) derived from the High Resolution Channel of the
Advanced Camera for Surveys on board the Hubble Space Telescope. In this work,
we apply to the NGC419 data the classical method of star formation history
(SFH) recovery via CMD reconstruction, deriving for the first time this
function for a star cluster with multiple turn-offs. The values for the cluster
metallicity, reddening, distance and binary fraction, were varied within the
limits allowed by present observations. The global best-fitting solution is an
excellent fit to the data, reproducing all the CMD features with striking
accuracy. The corresponding star formation rate is provided together with
estimates of its random and systematic errors. Star formation is found to last
for at least 700 Myr, and to have a marked peak at the middle of this interval,
for an age of 1.5 Gyr. Our findings argue in favour of multiple star formation
episodes (or continued star formation) being at the origin of the multiple main
sequence turn-offs in Magellanic Cloud clusters with ages around 1 Gyr. It
remains to be tested whether alternative hypotheses, such as a main sequence
spread caused by rotation, could produce similarly good fits to the data.
