The Madden‐Julian Oscillation (MJO) is a promising target for improving sub‐seasonal weather forecasts. Current forecast models struggle to simulate the MJO due to imperfect convective parameterizations and mean state biases, degrading their forecast skill. Previous studies have estimated a potential MJO predictability 5–15 days higher than current forecast skill, but these estimates also use models with parameterized convection. We perform a perfect‐model predictability experiment using a superparameterized global model in which the convective parameterization is replaced by a cloud resolving model. We add a second “silent” cloud resolving component to the control simulation that independently calculates convective‐scale processes using the same large‐scale forcings. The second set of convective states are used to initialize forecasts, representing uncertainty on the convective scale. We find a potential predictability of the MJO of 35–40 days in boreal winter using a single‐member ensemble forecast.