AgBiS2 nanocrystals have recently emerged as a RoHS compliant material for photovoltaics. This heavy-metal-free ternary chalcogenide can be prepared from earth-abundant precursors, is solution-processable and presents a high absorption coefficient as well as a suitable bandgap for solar cell applications. However, the full potential of AgBiS2 nanocrystals is yet to be realised; the highest efficiencies reported so far used very thin (~35 nm) absorbing layers due to the limited carrier transport and trap-assisted recombination that hinder the performance of thicker layers. In this work we implement a synthetic route to obtain larger size colloidal AgBiS2 nanocrystals, which in turn allows to fabricate thin film solar cells with higher mobility and reduced trap-assisted recombination, resulting in a power conversion efficiency of 6.4%, due to a photocurrent increase of 4 mA/cm2 compared to prior reports. We conclude by discussing on the main current challenges underpinning the photovoltaic performance of this material as well as strategies to further reduce the voltage and photocurrent losses.