The large majority of protoplanetary disks have very compact continuum emission (≲15 AU) at millimeter wavelengths. However, high angular resolution observations that resolve these small disks are still lacking, due to their intrinsically fainter emission compared with large bright disks. In this Letter we present 1.3 mm ALMA data of the faint disk (∼10 mJy) orbiting the TTauri star CX Tau at a resolution of ∼40 mas, ∼5 AU in diameter. The millimeter dust disk is compact, with a 68% enclosing flux radius of 14 AU, and the intensity profile exhibits a sharp drop between 10 and 20 AU, and a shallow tail between 20 and 40 AU. No clear signatures of substructure in the dust continuum are observed, down to the same sensitivity level of the DSHARP large program. However, the angular resolution does not allow us to detect substructures on the scale of the disk aspect ratio in the inner regions. The radial intensity profile closely resembles the inner regions of more extended disks imaged at the same resolution in DSHARP, but with no rings present in the outer disk. No inner cavity is detected, even though the disk has been classified as a transition disk from the spectral energy distribution in the near-infrared. The emission of ¹²CO is much more extended, with a 68% enclosing flux radius of 75 AU. The large difference of the millimeter dust and gas extents (> 5) strongly points to radial drift, and closely matches the predictions of theoretical models.