We are undertaking an ambitious proper motion survey of massive stars in the 30 Doradus region of the Large Magellanic Cloud using the unique capabilities of HST. We aim to derive the directions of motion of massive runaway stars, searching in particular for stars which have been ejected from the dense star cluster R136. These stars probe the dynamical processes in the core of the cluster. The core has been suggested as a formation site for very massive stars exceeding the canonical upper limit of the IMF. These are possible progenitors of intermediate-mass black holes. Furthermore, they provide insight about the origin of massive field stars, addressing open questions related to the poorly understood process of massive star formation. Some may originate from disrupted binary systems and bear the imprints of interaction with the original companion. They will end their life far away from their birth location as core collapse supernova or possibly even long gamma-ray bursts. Here we discuss the first epoch of observations, presenting a 16'x13' mosaic of the data, and initial results based on comparisons with archival data. SdM acknowledges the NASA Hubble Fellowship grant HST-HF-51270.01-A awarded by STScI, operated by AURA for NASA, contract NAS 5-26555.