We construct the supercurrent of the N = 1 supersymmetric Maxwell theory in ten dimensions. It contains 5760 + 5760 components. There exists a submultiplet of 5632 + 5632 components, which is a constrained d = 10 scalar superfield. The remaining 128 + 128 components form an off-shell multiplet with non-local transformation laws. The corresponding multiplet of fields has gauge transformations which suggest an underlying superconformal symmetry.