We present high spatial resolution images, at a wavelength of 6 cm, of the luminous blue variable star P Cygni. The images fully resolve the core of the stellar wind, and show that it is very clumpy. Two images were taken, separated in time by approximately a month, during which the structure in the wind has changed radically. The total flux observed has also changed significantly. We show that the clump sizes and electron densities are consistent with the radio variability being due to recombination of the ionized gas within the clumps, after key cooling lines become optically thin, causing the free-free emission to disappear. This is the first time that resolved radio images of a hot star wind have been obtained. It also represents important confirmation of a previous observation that thermal free-free wind emission can vary rapidly in a hot stellar wind
