We developed a system to reversibly encapsulate small numbers of molecules in an array of nanofabricated "dimples". This system enables highly parallel, long-term, and attachment-free studies of molecular dynamics via single-molecule fluorescence. In studies of bimolecular reactions of small numbers of confined molecules, we see phenomena that, while expected from basic statistical mechanics, are not observed in bulk chemistry. Statistical fluctuations in the occupancy of sealed reaction chambers lead to steady-state fluctuations in reaction equilibria and rates. These phenomena are likely to be important whenever reactions happen in confined geometries.