In this paper, we present an elegant solution to the 2D LIDAR-camera extrinsic calibration problem. Specifically, we develop a simple method for establishing correspondences between a line-scan (2D) LIDAR and a camera using a small calibration target that only contains a straight line. Moreover, we formulate the nonlinear least-squares problem for finding the unknown 6 degree-of-freedom (dof) transformation between the two sensors, and solve it analytically to determine its global minimum. Additionally, we examine the conditions under which the unknown transformation becomes unobservable, which can be used for avoiding ill-conditioned configurations. Finally, we present extensive simulation and experimental results for assessing the performance of the proposed algorithm as compared to alternative analytical approaches.