We report the observation of migrating chemotactic bands of Escherichia coli in a buffer solution. The temporal development of the bacterial density profile is observed by the scattered light intensity as the band migrates through a stationary laser beam. We have made a preliminary analysis of the observed band profile with help of the Keller-Segel theory. The model accounts for only some aspects of the observed time evolution of the density profile. The microscopic motility characteristics of the E. coli in the band are simultaneously studied by photon correlation. The measured correlation functions are analyzed to obtain the spatial dependence of the half-width within the band. A simple analytical model is proposed to account for the contribution of the twiddle motion to the correlation function. By analyzing the correlation function as a superposition of straight-line and twiddle motions, we obtain a satisfactory agreement between the theory and the measured angular dependence of the line shape. As a consequence we are able to extract a parameter beta, which measures the average fraction of twiddling bacteria in the center of the band at a given time.