We present Atacama Large Millimeter/Submillimeter Array observations of the rest-frame far-infrared (FIR) dust continuum emission of six bright Lyman-break galaxies (LBGs) at z ≃ 7. One LBG is detected (5.2σ at peak emission), whilst the others remain individually undetected at the 3σ level. The average FIR luminosity of the sample is found to be L_ FIR_ ≃2 ×1011 L☉, corresponding to an obscured star formation rate (SFR) that is comparable to that inferred from the unobscured UV emission. In comparison to the infrared excess (IRX =L_ FIR/L UV_)-β relation, our results are consistent with a Calzetti-like attenuation law (assuming a dust temperature of T = 40-50 K). We find a physical offset of 3 kpc between the dust continuum emission and the rest-frame UV light probed by Hubble Space Telescope imaging for galaxy ID65666 at z=7.17+0.09–0.06. The offset is suggestive of an inhomogeneous dust distribution, where 75 per cent of the total star formation activity (SFR ≃70 M☉/ yr) of the galaxy is completely obscured. Our results provide direct evidence that dust obscuration plays a key role in shaping the bright end of the observed rest-frame UV luminosity function at z ≃ 7, in agreement with cosmological galaxy formation simulations. The existence of a heavily obscured component of galaxy ID65666 indicates that dusty star-forming regions, or even entire galaxies, that are 'UV dark' are significant even in the z ≃ 7 galaxy population.