2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59241This note is a sequel to "Gerbes of chiral differential operators. II", math.AG/0003170. We study gerbes of chiral differential operators acting on the exterior algebra $ΛE$ of a vector bundle over a smooth algebraic variety $X$. When $E=Ω^1_X$ this gerbe admits a canonical global section which coincides with the chiral de Rham complex of $X$.26 pages, Tex. List of references corrected. Please use this versionAlgebraic Geometrytext