This article introduces a chemical kinetic model of the transcriptional elongation dynamics of RNA polymerase. The model's novel concept is a look-ahead feature, in which nucleotides bind reversibly to the DNA before being incorporated covalently into the nascent RNA chain. Analytical and computational methods for studying the behavior of the look-ahead model are introduced, and several approaches to parameter estimation are tested on synthetic and also on actual experimental data. Two types of experimental data are considered: 1), the mean velocity of RNA polymerase as a function of the ambient concentrations of the ribonucleoside triphosphates; and 2), the distribution of time intervals between the forward steps of RNA polymerase. By separately fitting the look-ahead model to these two types of data, we obtain estimates of the model parameters. The most difficult parameter to estimate is the width of the look-ahead window. Both types of data suggest a small window size, but the second type does a better job of distinguishing the different window sizes. These latter data rule out a window size of 1, and they strongly suggest a look-ahead window that is approximately four bases in width. Additional experiments to determine the window size are proposed.