We present the results of high velocity (1.3 km s(-1) channels) and high spatial (similar to 5", or similar to 250 pc at the distance of I Zw 18) resolution H I synthesis observations of the blue compact dwarf galaxy I Zw 18 to investigate the link between its unique evolutionary history and the neutral gas distribution and kinematics. The H I distribution is extensive, with diffuse neutral gas extending to the northwest and south of the main component. This diffuse gas may be a remnant of the nascent H I cloud. The kinematics of the I Zw 18 system are complex, with four components identified: H I-A, H I-C, H I-I, and H I-SX. The gas associated with the main body, H I-A, has a steep velocity gradient; although our analysis is hindered by poor spatial resolution relative to the extent of the system, the main body appears to be undergoing solid-body rotation. The optical condensation to the northwest of I Zw 18 is embedded in the common H I envelope and is found to be kinematically separate from the main body at a velocity of 740 km s(-1) (H I-C). The interbody gas, H I-I, connects H I-A and H I-C. Finally, a large, diffuse, kinematically distinct gas component extends at least 1' to the south of the main body (H I-SX), with no known optical counterpart. The peak of the gas column density coincides with the southeast H II region in the main body; two other H I peaks are associated with the northwest H II region and an H It region in the optical condensation to the northwest. In many respects, the H I properties of the main body of I ZW 18 (H I-A) are not unusual for dwarf galaxies; the peak column density, gas dispersion, M-H/L-B, and M-H/M-T are remarkably similar to other low-mass systems. The neutral gas associated with I Zw 18 is best described as a fragmenting H I cloud in the early stages of galaxy evolution. The derived gas distribution and kinematics are placed in the context of the known star formation history of I Zw 18. In particular, the neutral gas velocity dispersion is critical for calculating the abundance of the O I cloud detected by the Hubble Space Telescope. While significantly affected by beam smearing in the presence of a steep velocity gradient, the derived gas velocity dispersion in the main body of I Zw 18 is approximately 12-14 km s(-1). Based on the present analysis, the O I cloud has an oxygen abundance greater than or similar to 1/60 of solar, indicating that both the neutral and ionized mediums are well mixed.
