Symmetry-breaking interactions have a crucial role in many areas of physics, ranging from classical ferrofluids to superfluid 3He and d-wave superconductivity. For superfluid quantum gases, a variety of new physical phenomena arising from the symmetry-breaking interaction between electric or magnetic dipoles are expected1. Novel quantum phases in optical lattices, such as chequerboard or supersolid phases, are predicted for dipolar bosons2, 3. Dipolar interactions can also enrich considerably the physics of quantum gases with internal degrees of freedom4, 5, 6. Arrays of dipolar particles could be used for efficient quantum information processing7. Here we report the realization of a chromium Bose–Einstein condensate with strong dipolar interactions. By using a Feshbach resonance, we reduce the usual isotropic contact interaction, such that the anisotropic magnetic dipole–dipole interaction between 52Cr atoms becomes comparable in strength. This induces a change of the aspect ratio of the atom cloud; for strong dipolar interactions, the inversion of ellipticity during expansion (the usual 'smoking gun' evidence for a Bose–Einstein condensate) can be suppressed. These effects are accounted for by taking into account the dipolar interaction in the superfluid hydrodynamic equations governing the dynamics of the gas, in the same way as classical ferrofluids can be described by including dipolar terms in the classical hydrodynamic equations. Our results are a first step in the exploration of the unique properties of quantum ferrofluids.