Single-molecule fluorescence techniques(1-3) are key for a number of applications, including DNA sequencing(4,5), molecular and cell biology(6,7) and early diagnosis(8). Unfortunately, observation of single molecules by diffraction-limited optics is restricted to detection volumes in the femtolitre range and requires pico- or nanomolar concentrations, far below the micromolar range where most biological reactions occur(2). This limitation can be overcome using plasmonic nanostructures, which enable the confinement of light down to nanoscale volumes(9-13). Although these nanoantennas enhance fluorescence brightness(14-20), large background signals(20-22) and/or unspecific binding to the metallic surface(23-25) have hampered the detection of individual fluorescent molecules in solution at high concentrations. Here we introduce a novel 'antenna-in-box' platform that is based on a gap-antenna inside a nanoaperture. This design combines fluorescent signal enhancement and background screening, offering high single-molecule sensitivity (fluorescence enhancement up to 1,100-fold and microsecond transit times) at micromolar sample concentrations and zeptolitre-range detection volumes. The antenna-in-box device can be optimized for single-molecule fluorescence studies at physiologically relevant concentrations, as we demonstrate using various biomolecules.