We present high–resolution ( 0.16 ^ { \prime \prime } ) 870 \mu m Atacama Large Millimeter/submillimeter Array ( ALMA ) imaging of 16 luminous ( L _ { IR } \sim 4 \times 10 ^ { 12 } L _ { \odot } ) submillimeter galaxies ( SMGs ) from the ALESS survey of the Extended Chandra Deep Field South . This dust imaging traces the dust–obscured star formation in these z \sim 2.5 galaxies on \sim 1.3 kpc scales . The emission has a median effective radius of R _ { e } = 0.24 ^ { \prime \prime } \pm 0.02 ^ { \prime \prime } , corresponding to a typical physical size of R _ { e } = 1.8 \pm 0.2 kpc . We derive a median Sérsic index of n = 0.9 \pm 0.2 , implying that the dust emission is remarkably disk-like at the current resolution and sensitivity . We use different weighting schemes with the visibilities to search for clumps on 0.12 ^ { \prime \prime } ( \sim 1.0 kpc ) scales , but we find no significant evidence for clumping in the majority of cases . Indeed , we demonstrate using simulations that the observed morphologies are generally consistent with smooth exponential disks , suggesting that caution should be exercised when identifying candidate clumps in even moderate S/N interferometric data . We compare our maps to comparable–resolution HST H _ { 160 } -band images , finding that the stellar morphologies appear significantly more extended and disturbed , and suggesting that major mergers may be responsible for driving the formation of the compact dust disks we observe . The stark contrast between the obscured and unobscured morphologies may also have implications for SED fitting routines that assume the dust is co-located with the optical/near–IR continuum emission . Finally , we discuss the potential of the current bursts of star formation to transform the observed galaxy sizes and light profiles , showing that the z \sim 0 descendants of these SMGs are expected to have stellar masses , effective radii , and gas surface densities consistent with the most compact massive ( M _ { * } \sim 1–2 \times 10 ^ { 11 } M _ { \odot } ) early–type galaxies observed locally . Key words : galaxies : starburst – galaxies : high-redshift – submillimeter – catalogs