WWe present evidence for stochastic star formation histories in low-mass (M* <1010M⊙) galaxies from observations within the Galaxy And Mass Assembly (GAMA) survey. For ̃73 000 galaxies between 0.05 < z < 0.32, we calculate star formation rates (SFR) and specific star formation rates (SSFR = SFR/M*) from spectroscopic Hα measurements and apply dust corrections derived from Balmer decrements. We find a dependence of SSFR on stellar mass, such that SSFRs decrease with increasing stellar mass for star-forming galaxies, and for the full sample, SSFRs decrease as a stronger function of stellar mass. We use simple parametrizations of exponentially declining star formation histories to investigate the dependence on stellar mass of the star formation time-scale and the formation redshift. We find that parametrizations previously fit to samples of z ̃ 1 galaxies cannot recover the distributions of SSFRs and stellar masses observed in the GAMA sample between 0.05 < z <0.32. In particular, a large number of low-mass (M* < 1010M⊙) galaxies are observed to have much higher SSFRs than can be explained by these simple models over the redshift range of 0.05 < z < 0.32, even when invoking mass-dependent staged evolution. For such a large number of galaxies to maintain low stellar masses, yet harbour such high SSFRs, requires the late onset of a weak underlying exponentially declining star formation history with stochastic bursts of star formation superimposed.