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 EUV dimmings and post-eruptive arcades are hard to identify for stealth CMEs and require extensive image processing techniques. These weak observational signatures mean 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 3 March 2011 occurred. The magnetic field prior to the eruption is evaluated using a Linear Force Free Field (LFFF) model and a Potential Field Source Surface (PFSS) model, and complemented by in-depth observational analysis. The models are verified using observations of plasma emission structures in the stealth CME source region and trans-equatorial loops. We find evidence of a high-altitude null point in both the LFFF model and the PFSS model, with surrounding field lines connecting two active regions on the solar disk. One of these active regions in the Southern Hemisphere is shown to be the source region of the stealth CME. Three distinct episodes of flare ribbon formation are observed in AIA 304Å. Two occurred prior to the eruption and suggest the occurrence of magnetic reconnection that builds the eruptive structure. The third occurs at the same time as an erupting cavity is observed in STEREO-B 171Å data; this subsequently becomes part of the propagating CME observed in COR1. We conclude that reconnection at the null point, driven by eruptive activity in the complex northern active region, aids the eruption of the stealth CME by removing field that acted to stabilise the pre-eruptive structure.