Single-molecule measurements are a valuable tool for revealing details of enzyme mechanisms by enabling observation of unsynchronized behavior. However, this approach often requires immobilizing the enzyme on a substrate, a process which may alter enzyme behavior. We apply a microfluidic trapping device to allow, for the first time, prolonged solution-phase measurement of single enzymes in solution. Individual redox events are observed for single molecules of a blue nitrite reductase and are used to extract the microscopic kinetic parameters of the proposed catalytic cycle. Changes in parameters as a function of substrate concentration are consistent with a random sequential substrate binding mechanism.