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The possibility of cloaking an object from detection by electromagnetic waves has recently become a topic of considerable interest. The design of a cloak uses transformation optics, in which a conformal coordinate transformation is applied to Maxwell's equations to obtain a spatially distributed set of constitutive parameters that define the cloak. Here, we present an experimental realization of a cloak design that conceals a perturbation on a flat conducting plane, under which an object can be hidden. To match the complex spatial distribution of the required constitutive parameters, we constructed a metamaterial consisting of thousands of elements, the geometry of each element determined by an automated design process. The ground-plane cloak can be realized with the use of nonresonant metamaterial elements, resulting in a structure having a broad operational bandwidth (covering the range of 13 to 16 gigahertz in our experiment) and exhibiting extremely low loss. Our experimental results indicate that this type of cloak should scale well toward optical wavelengths.