We report the analysis of the first superburst from a transiently accreting neutron star system with the All-Sky Monitor (ASM) on the Rossi X-ray Timing Explorer. The superburst occurred 55 days after the onset of an accretion outburst in 4U 1608-522. During that time interval, the accretion rate was at least 7% of the Eddington limit. The peak flux of the superburst is 22 to 45% of the Eddington limit, and its radiation energy output is between 4e41 and 9e41 erg for a distance of 3.2 kpc. Fits of cooling models to the superburst light curve indicate an ignition column depth between 1.5e12 and 4.1e12 g/cm2. Extrapolating the accretion history observed by the ASM, we derive that this column was accreted over a period of 26 to 72 years. The superburst characteristics are consistent with those seen in other superbursting low-mass X-ray binaries. However, the transient nature of the hosting binary presents significant challenges for superburst theory, requiring additional ingredients for the models. The carbon that fuels the superburst is thought to be produced mostly during the accretion outbursts and destroyed in the frequent type-I X-ray bursts. Mixing and sedimentation of the elements in the neutron star envelope may significantly influence the balance between the creation and destruction of carbon. Furthermore, predictions for the temperature of the neutron star crust fail to reach the values required for the ignition of carbon at the inferred column depth.