The stability of a one-dimensional weak D-type ionization front is investigated, in case the perturbations of the neutral gas and ionized gas on the two sides of the front are isothermal. The characteristic value problem governing the complex rates of growth for the unstable modes is formulated, and the solutions for the rates of growth are obtained in the limit that the ratio of the speed of sound in the neutral gas to the speed of sound in the ionized gas tends to zero. If the radiation field associated with the front has no particular symmetry, both overstable and unstable modes occur; if the symmetry of the radiation field is such that the flux through every plane normal to the front vanishes, then all modes are simply unstable. If the radiation field has this symmetry and the condition of the front is D-critical (in the nomenclature of Kahn), the front is stable. However, even small departures of the condition of the front from D-critical will allow a substantial instability. For this reason, the stability of the critical D-type front probably has no important consequences. The physical mechanism for the instability is considered briefly, and it is shown that the instability is related to such well-known processes as the rocket effect of Oort and Spitzer. As a numerical example illustrating the theory, the rates of growth are computed for the instability of the boundary of an H ii region illuminated by a star of early spectral type. A conclusion tentatively drawn from this example is that the instability might produce irregularities similar to bright rims and "elephant trunks" in a time comparable to the age of the H ii region.