Context: Large cavities in disks are important testing grounds for the mechanisms proposed to drive disk evolution and dispersion, such as dynamical clearing by planets and photo-evaporation. Aims: We aim to resolve the large cavity in the disk around HD 34282, such as has been predicted by previous studies modeling the spectral energy distribution Methods: Using ALMA band 7 observations we study HD 34282 with a spatial resolution of 0.10arcsec x 0.17arcsec at 345 GHz. Results: We resolve the disk around HD 34282 into a ring between 0.24arcsec and 1.15arcsec (78 and 374 au adopting a distance of 325 pc). The emission in this ring shows azimuthal asymmetry centered at a radial distance of 0.46arcsec and a position angle of 135 degrees and an azimuthal FWHM of 51 degrees. We detect CO emission both inside the disk cavity and as far out as 2.7 times the radial extent of the dust emission. Conclusions: Both the large disk cavity and the azimuthal structure in the disk around HD 34282 can be explained by the presence of a 50 jupiter mass brown dwarf companion at a separation of ~ 0.1arcsec.