Résumé : Luminous blue variables (LBVs) are massive stars caught in a post-main sequence phase, during which they lose a significant amount of mass. Since, on one hand, it is thought that the majority of massive stars are close binaries that will interact during their lifetime, and on the other, the most dramatic example of an LBV, η Car, is a binary, it would be useful to find other binary LBVs. We present here interferometric observations of the LBV HR Car done with the AMBER and PIONIER instruments attached to ESO's Very Large Telescope Interferometer (VLTI). Our observations, spanning two years, clearly reveal that HR Car is a binary star. It is not yet possible to fully constrain the orbit, and the orbital period may lie between a few years and several hundred years. We derive a radius for the primary in the system and possibly also resolve the companion. The luminosity ratio in the H-band between the two components is changing with time, going from about 6 to 9. We also tentatively detect the presence of some background flux which remained at the 2% level until January 2016, but then increased to 6% in April 2016. Our AMBER results show that the emission line-forming region of Brγ is more extended than the continuum-emitting region as seen by PIONIER and may indicate some wind-wind interaction. Most importantly, we constrain the total masses of both components, with the most likely range being 33.6 MȮ and 45 MȮ. Our results show that the LBV HR Car is possibly an η Car analog binary system with smaller masses, with variable components, and further monitoring of this object is definitively called for.