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Methods for accurately quantifying the concentration of a particular analyte in solution are all based on ensemble responses in which many analyte molecules give rise to the measured signal. In this paper, single molecules of β-galactosidase were monitored using a 1 mm diameter fiber optic bundle with 2.4 × 10⁵ individually sealed, femtoliter microwell reactors. By observation of the buildup of fluorescent products from single enzyme molecule catalysis over the array of reaction vessels and by application of a Poisson statistical analysis, a digital concentration readout was obtained. This approach should prove useful for single molecule enzymology and ultrasensitive bioassays. More generally, the ability to determine concentration by counting individual molecules offers a new approach to analysis of dilute solutions.