  The observed radial and vertical metallicity distribution of old stars in the
Milky Way disk provides a powerful constraint on the chemical enrichment and
dynamical history of the disk. We present the radial metallicity gradient,
\Delta[Fe/H]/\Delta R, as a function of height above the plane, |Z|, using 7010
main sequence turnoff stars observed by the Sloan Extension for Galactic
Understanding and Exploration (SEGUE) survey. The sample consists of mostly old
thin and thick disk stars, with a minimal contribution from the stellar halo,
in the region 6 < R < 16 kpc, 0.15 < |Z| < 1.5 kpc. The data reveal that the
radial metallicity gradient becomes flat at heights |Z| > 1 kpc. The median
metallicity at large |Z| is consistent with the metallicities seen in outer
disk open clusters, which exhibit a flat radial gradient at [Fe/H] ~ -0.5. We
note that the outer disk clusters are also located at large |Z|; because the
flat gradient extends to small R for our sample, there is some ambiguity in
whether the observed trends for clusters are due to a change in R or |Z|. We
therefore stress the importance of considering both the radial and vertical
directions when measuring spatial abundance trends in the disk. The flattening
of the gradient at high |Z| also has implications on thick disk formation
scenarios, which predict different metallicity patterns in the thick disk. A
flat gradient, such as we observe, is predicted by a turbulent disk at high
redshift, but may also be consistent with radial migration, as long as mixing
is strong. We test our analysis methods using a mock catalog based on the model
of Sch\"onrich & Binney, and we estimate our distance errors to be ~25%. We
also show that we can properly correct for selection biases by assigning
weights to our targets.
