Interest in stealth coronal mass ejections (CMEs) is increasing due to their relatively high occurrence rate and space weather impact. However, typical CME signatures such as extreme-ultraviolet dimmings and post-eruptive arcades are hard to identify and require extensive image processing techniques. These weak observational signatures mean that little is currently understood about the physics of these events. We present an extensive study of the magnetic field configuration in which the stealth CME of 2011 March 3 occurred. Three distinct episodes of flare ribbon formation are observed in the stealth CME source active region (AR). Two occurred prior to the eruption and suggest the occurrence of magnetic reconnection that builds the structure that will become eruptive. The third occurs in a time close to the eruption of a cavity that is observed in STEREO-B 171 Å data; this subsequently becomes part of the propagating CME observed in coronagraph data. We use both local (Cartesian) and global (spherical) models of the coronal magnetic field, which are complemented and verified by the observational analysis. We find evidence of a coronal null point, with field lines computed from its neighborhood connecting the stealth CME source region to two ARs in the northern hemisphere. We conclude that reconnection at the null point aids the eruption of the stealth CME by removing the field that acted to stabilize the preeruptive structure. This stealth CME, despite its weak signatures, has the main characteristics of other CMEs, and its eruption is driven by similar mechanisms.