We report and demonstrate a new technique to measure the full intensity and phase of a single femtosecond laser pulse. The technique, which we call 'frequency resolved optical gating' (FROG), is inexpensive, easy to implement, and provides an output that graphically displays the instantaneous frequency vs. time of the pulse. Using almost any instantaneous nonlinear- optical interaction of two replicas of the ultrashort pulse to be measured, FROG involves measuring the spectrum of the signal pulse as a function of delay between the two replicas. The resulting trace of intensity vs. frequency and delay yields an intuitive display of the pulse, similar to the pulse spectrogram. We show that the problem of inverting the FROG trace to obtain the pulse intensity and phase is a two-dimensional phase-retrieval problem. As a result, the FROG trace yields, in principle, an essentially unique pulse intensity and phase. In this work, we show that this is the case in practice, also. In addition, we present an iterative- Fourier-transform algorithm for inverting the FROG trace.