  Ultra-short-period (USP) planets reside inside the expected truncation radius
for typical T Tauri disks. As a result, their current orbital locations require
an explanation beyond standard disk migration or in situ formation. Modern
theories of planet-disk interactions indicate that once a planet migrates close
to the disk's inner truncation radius, Type I torques vanish or switch
direction, depending on the stellar and disk conditions, so that the planet is
expected to stop its orbital decay and become trapped. In this work, we show
that that magnetically-driven sub-Keplerian gas flow in the inner disk can
naturally counteract these effects and produce systems with USP planets at
their observed orbital radii. The sub-Keplerian gas flow provides a headwind to
small planets, and the resulting torque can overcome the effects of outward
Type I migration near the co-rotation radius. For suitable disk and planet
parameters, the torques due to the sub-Keplerian gas flow lead to inward
migration on a rapid timescale. Over the time span of an FU Ori outburst, which
moves the disk truncation radius inward, the rapid headwind migration can place
planets in USP orbits. The combination of headwind migration and FU Ori
outbursts thus provides a plausible mechanism to move small planets from
$a=0.05-0.1$ AU down to $a=0.01-0.02$ AU. This effect is amplified for low-mass
planets, consistent with existing observations.
