We present the discovery of a luminous unresolved H II complex on the edge of dwarf galaxy GAMA J141103.98-003242.3 using data from the Sydney-AAO Multi-object Integral field spectrograph (SAMI) Galaxy Survey. This dwarf galaxy is situated at a distance of ~100 Mpc and contains an unresolved region of H II emission that contributes ~70 per cent of the galaxy's H_alpha luminosity, located at the top end of established H II region luminosity functions. For the H II complex, we measure a star-formation rate of 0.147\pm0.041 M_solar yr^-1 and a metallicity of 12+log(O/H) = 8.01\pm0.05 that is lower than the rest of the galaxy by ~0.2 dex. Data from the H I Parkes All-Sky Survey (HIPASS) indicate the likely presence of neutral hydrogen in the galaxy to potentially fuel ongoing and future star-forming events. We discuss various triggering mechanisms for the intense star-formation activity of this H II complex, where the kinematics of the ionised gas are well described by a rotating disc and do not show any features indicative of interactions. We show that SAMI is an ideal instrument to identify similar systems to GAMA J141103.98-003242.3, and the SAMI Galaxy Survey is likely to find many more of these systems to aid in the understanding of their formation and evolution.