H I absorption observations toward the H II region Orion A are presented. The observations, obtained with the VLA in the C-configuration, have an angular resolution of 18″ and a velocity resolution of 0.64 km s-1. Three large-scale and five small-scale H I components have been detected in absorption toward the continuum of the H II region. In this paper only the five small-scale components, which were not previously recognized, are discussed. These components are located around the core of the H II region. All except one are blueshifted by ∼15 km s-1 with respect to the ambient neutral gas. Several lines of evidence indicate that the small-scale components are physically associated with the H II region. The anomalous velocities of H I clumps are caused by rocket acceleration due to anisotropic ionization or to acceleration by high-velocity ionized material in the H II region. The neutral clumps may be interpreted as density enhancements in the neutral gas near the ionization front, or as fragments of a layer of neutral gas that existed in front of the H II region before the ionized gas broke through the boundary of the molecular cloud. An analysis of the effects of rocket acceleration and a simple scenario for the evolution of the neutral clumps is presented. It is shown that only clumps of the observed density undergo appreciable rocket acceleration. More tenuous gas is rapidly ionized while the ionization of denser clumps is so slow that the rocket effect is unimportant. It is suggested that the clumps may be transient phenomena, that are currently expanding and dissolving into the ambient medium of the H II region.