On 9 June 1988, Pluto occulted a 12th magnitude star1. Several observations of the occultation were obtained from Australia, New Zealand, and the south Pacific2 and indicated that the initial decline in stellar flux was gradual, as would be expected if the starlight was defocused by an extended atmosphere around the planet. Here we interpret data obtained from the 1- telescope at the University of Tasmania, Hobart, in terms of a theory for occultation by an atmosphere whose thickness is comparable to the planetary radius. The data can be satisfactorily fitted with a methane atmosphere at plausible pressures and temperatures. The surface pressures inferred from this single chord are uncertain by an order of magnitude, but are consistent with spectroscopic constraints.