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We present an experimental demonstration of strong coupling between a surface plasmon propagating on a planar silver substrate, and the lowest excited state of CdSe nanocrystals. Variable-angle spectroscopic ellipsometry measurements demonstrated the formation of plasmon-exciton mixed states, characterized by a Rabi splitting of $\sim$ 82 meV at room temperature. Such a coherent interaction has the potential for the development of plasmonic non-linear devices, and furthermore, this system is akin to those studied in cavity quantum electrodynamics, thus offering the possibility to study the regime of strong light-matter coupling in semiconductor nanocrystals at easily accessible experimental conditions.