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<jats:title>ABSTRACT</jats:title> <jats:p>We analyze the extreme high-magnification microlensing event OGLE-2008-BLG-279, which peaked at a maximum magnification of <jats:italic>A</jats:italic> ∼ 1600 on 2008 May 30. The peak of this event exhibits both finite-source effects and terrestrial parallax, from which we determine the mass of the lens, <jats:italic>M<jats:sub>l</jats:sub> </jats:italic> = 0.64 ±  0.10 <jats:italic>M</jats:italic> <jats:sub>☉</jats:sub>, and its distance, <jats:italic>D<jats:sub>l</jats:sub> </jats:italic> = 4.0 ±  0.6 kpc. We rule out Jupiter-mass planetary companions to the lens star for projected separations in the range 0.5–20 AU. More generally, we find that this event was sensitive to planets with masses as small as <jats:inline-formula> <jats:tex-math><?CDATA $0.2 \;M_\oplus \simeq 2 \;M_{\rm {Mars}}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apj326622ieqn1.gif" xlink:type="simple" /> </jats:inline-formula> with projected separations near the Einstein ring (∼3 AU).</jats:p>