One of the primary goals of the spin physics program at the STAR experiment is to constrain the polarized gluon distribution function, [delta]g(X,Q2), by measuring the double longitudinal spin asymmetry, ALL, of various final-state channels. Neutral pions provide a potentially powerful final state because they are copiously produced in p+p collisions and have few backgrounds. In 2009, STAR took 14 pb-1 of integrated luminosity of 200 GeV p+p collisions, with average beam longitudinal polarization of 59%. Neutral pions produced in these collisions can be identified using STAR's large-acceptance electromagnetic calorimeter, with help from tracking from the STAR Time Projection Chamber. This work presents a measurement of the inclusive neutral pion ALL from this data, based on a new [pi]0 reconstruction algorithm. A comparison to theoretical predictions and other experimental results suggests that the current best-fit value of AG, the gluon contribution to the proton spin, is too small and that [delta]G is actually comparable in magnitude to the quark contribution to the proton spin [delta][sigma].