We present high-resolution submillimeter interferometric imaging of two of the brightest high-redshift submillimeter galaxies known: GN 20 and AzTEC1 at 0.8 super(image )and 0.3 super(image ) resolution, respectively. Our data-the highest resolution submillimeter imaging of high-redshift sources accomplished to date-were collected in three different array configurations: compact, extended, and very extended. We derive angular sizes of 0.6 super(image ) and 1.0 super(image ) for GN 20 and 0.3 super(image ) and 0.4 super(image ) for AzTEC1 from modeling their visibility functions as a Gaussian and an elliptical disk, respectively. Because both sources are B-band dropouts, they likely lie within a relatively narrow redshift window around image, which indicates their angular extent corresponds to physical scales of 4-8 and 1.5-3 kpc, respectively, for the starburst region. By way of a series of simple assumptions, we find preliminary evidence that these hyperluminous starbursts-with star formation rates >1000 image yrimage -are radiating at or close to their Eddington limit. Should future high-resolution observations indicate that these two objects are typical of a population of high-redshift Eddington-limited starbursts, this could have important consequences for models of star formation and feedback in extreme environments.