Taming quantum dynamical processes is the key to novel applications of quantum physics, e.g. in quantum information science. The control of light-matter interactions at the single-atom and single-photon level can be achieved in cavity quantum electrodynamics, in particular in the regime of strong coupling where atom and cavity form a single entity. In the optical domain, this requires permanent trapping and cooling of an atom in a micro-cavity. We have now realized three-dimensional cavity cooling and trapping for an orthogonal arrangement of cooling laser, trap laser and cavity vacuum. This leads to average single-atom trapping times exceeding 15 seconds, unprecedented for a strongly coupled atom under permanent observation.