This paper presents a new algorithm for the extrinsic calibration of a perspective camera and an invisible 2D laser-rangefinder (LRF). The calibration is achieved by freely moving a checkerboard pattern in order to obtain plane poses in camera coordinates and depth readings in the LRF reference frame. The problem of estimating the rigid displacement between the two sensors is formulated as one of registering a set of planes and lines in the 3D space. It is proven for the first time that the alignment of three plane-line correspondences has at most eight solutions that can be determined by solving a standard p3p problem and a linear system of equations. This leads to a minimal closed-form solution for the extrinsic calibration that can be used as hypothesis generator in a RANSAC paradigm. Our calibration approach is validated through simulation and real experiments that show the superiority with respect to the current state-of-the-art method requiring a minimum of five input planes.