We demonstrate strong coupling between a surface plasmon and intersublevel transitions in self-assembled InAs quantum dots. The surface plasmon mode exists at the interface between the semiconductor emitter structure and a periodic array of holes perforating a metallic Pd/Ge/Au film that also serves as the top electrical contact for the emitters. Spectrally narrowed quantum-dot electroluminescence was observed for devices with varying subwavelength hole spacing. Devices designed for 9, 10, and 11 μm wavelength emission also exhibit a significant spectral splitting. The association of the splitting with quantum-dot Rabi oscillation is consistent with results from a calculation of spontaneous emission from an interacting plasmonic field and quantum-dot ensemble. The fact that this Rabi oscillation can be observed in an incoherently excited, highly inhomogeneously broadened system demonstrates the utility of intersublevel transitions in quantum dots for investigations of coherent transient and quantum coherence phenomena.