We experimentally demonstrate dramatically enhanced light-matter interaction for molecules placed inside the nanometer scale gap of a plasmonic waveguide. We observe spontaneous emission rate enhancements of up to about 60 times due to strong optical localization in two dimensions. This rate enhancement is a nonresonant nature of the plasmonic waveguide under study overcoming the fundamental bandwidth limitation of conventional devices. Moreover, we show that about 85% of molecular emission couples into the waveguide highlighting the dominance of the nanoscale optical mode in competing with quenching processes. Such optics at molecular length scales paves the way toward integrated on-chip photon source, rapid transfer of quantum information, and efficient light extraction for solid-state-lighting devices.