We have measured the relaxation time, T1, of the spin of a single electron confined in a semiconductor quantum dot. In a magnetic field, applied parallel to the two-dimensional electron gas in which the quantum dot is defined, splitting of the orbital states due to Zeeman energy is directly observed by electron transport measurements. By applying short pulses we can populate the excited spin state with one electron and monitor the relaxation of the spin. We find a lower bound on T1 of 50 microseconds at 7.5 T. The real T1 may be much longer than this lower bound. A continuous charge measurement on the dot has no observable effect on the spin relaxation.