The origin of massive field stars in the Large Magellanic Cloud (LMC) has long been an enigma. The recent measurements of large offsets (~100 km/s) between the heliocentric radial velocities of some very massive (O2-type) field stars and the systemic LMC velocity provides a possible explanation of this enigma and suggests that the field stars are runaway stars ejected from their birth places at the very beginning of their parent clusters dynamical evolution. A straightforward way to prove this explanation is to measure the proper motions of the field stars and to show that they are moving away from one of the nearby star clusters or OB associations. This approach however is complicated by the large distance to the LMC, which makes accurate proper motion measurements difficult. We use an alternative approach for solving the problem, based on the search for bow shocks produced by runaway stars. The geometry of detected bow shocks would allow us to infer the direction of stellar motion and thereby to determine their possible parent clusters. In this paper we present the results of a search for bow shocks around six massive field stars which were suggested in the literature as candidate runaway stars. Using archival (Spitzer Space Telescope) data, we found a bow shock associated with one of our program stars, the O2 V((f*)) star BI 237, which is the first-ever detection of bow shocks in the LMC. Orientation of the bow shock suggests that BI 237 was ejected from the OB association LH 82 (located at ~120 pc in projection from the star). A by-product of our search is the detection of bow shocks generated by four OB stars in the field of the LMC and an arc-like structure attached to the candidate luminous blue variable R81 (HD 269128). The geometry of two of these bow shocks is consistent with the possibility that their associated stars were ejected from the 30 Doradus star forming complex.
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