Rossby wave trains associated with the Madden-Julian Oscillation (MJO) tropical intraseasonal variability were analyzed using ERA5 composites arranged according to active phases of the MJO. During austral winter under neutral El Niño Southern Oscillation conditions, positive precipitation anomalies in Chile from 30$^\circ$ to 45$^\circ$S coincide with strong real-time multivariate MJO (RMM) phase 1 events. We found that a three-part mechanism, traced approximately 10 to 15 days before MJO phase 1 events, roughly corresponding to RMM phases 7 and 8, explains these precipitation anomalies. This mechanism is composed of three Rossby wave trains in response to convective perturbations: two interhemispheric teleconnections attributed to suppressed convection in the Indian Ocean and the Maritime Continent, and a cross-hemispheric Rossby wave linked to enhanced convection over the warm pool of the western hemisphere. Composite analyses of OLR and wave activity flux, complemented with Rossby wave ray tracing, support these findings. This research provides insights into the MJO’s influence on additional large-scale teleconnection patterns across the Southern Hemisphere besides the Pacific South American (PSA) teleconnection mode. The dispersion of the convective RMM phase at different lags and the interaction between multiple wave trains introduce uncertainty when associating a specific RMM phase with precipitation anomalies.