We have measured the angular diameter of the transiting extrasolar planet host star HD 189733 using the CHARA O/IR interferometric array. Combining our new angular diameter of 0.377+/-0.024 mas with the Hipparcos parallax leads to a linear radius for the host star of 0.779+/-0.052 Rsol and a radius for the planet of 1.19+/-0.08 RJup. Adopting the mass of the planet as derived by its discoverers, we derive a mean density of the planet of 0.91+/-0.18 g cm-3. This is the first determination of the diameter of an extrasolar planet through purely direct means.