A thorough analysis of the OGLE-II time-series photometry of the Large Magellanic Cloud bar supplemented by similar data from the MACHO database led us to the discovery of three β Cephei-type stars. These are the first known extragalactic β Cephei-type stars. Two of the three stars are multiperiodic. Two stars have inferred masses of about 10M☉ while the third is about 2mag brighter and at least twice as massive. All three variables are located in or very close to the massive and young LMC associations (LH41, 59 and 81). It is therefore very probable that the variables have higher than average metallicities. This would reconcile our finding with theoretical predictions of the shape and location of the β Cephei instability strip in the H-R diagram. The low number of β Cephei stars found in the LMC is another observational confirmation of strong dependence of the mechanism driving pulsations in these variables on metallicity. Follow-up spectroscopic determination of the metallicities in the discovered variables will provide a good test for the theory of pulsational stability in massive main-sequence stars.