Contact is at the core of robotic manipulation. At times, it is desired (e.g. manipulation and grasping), and at times, it is harmful (e.g. when avoiding obstacles). However, traditional path planning algorithms focus solely on collision-free paths, limiting their applicability in contact-rich tasks. To address this limitation, we propose the domain of Language-Conditioned Path Planning, where contact-awareness is incorporated into the path planning problem. As a first step in this domain, we propose Language-Conditioned Collision Functions (LACO) a novel approach that learns a collision function using only a single-view image, language prompt, and robot configuration. LACO predicts collisions between the robot and the environment, enabling flexible, conditional path planning without the need for manual object annotations, point cloud data, or ground-truth object meshes. In both simulation and the real world, we demonstrate that LACO can facilitate complex, nuanced path plans that allow for interaction with objects that are safe to collide, rather than prohibiting any collision.