The concept of distance used in binary array representations of images is adapted to a quadtree representation. The chessboard distance metric is shown to be particularly suitable for the quadtree. A chessboard distance transform for a quadtree is defined as the minimum distance in the plane from each BLACK node to the border of a WHiTE node. An algorithm is presented which computes this transform by only examining the BLACK node's adjacent and abutting neighbors and their progeny. However, unlike prior work with quadtrees, computation of the distance transform requires a capability of finding neighbors in the diagonal direction rather than merely in the horizontal and vertical directions. The algorithm's average execution time is proportional to the number of leaf nodes in the quadtree.