Weyl nodes can be classified into zero-dimensional (0D) Weyl points, 1D Weyl nodal lines, and 2D Weyl nodal surfaces (WNS), which possess finite Chern numbers. Up to date, the largest Chern number of WPs identified in Weyl semimetals is 4, which is thought to be a maximal value for linearly crossing points in solids. On the other hand, whether the Chern numbers of nonzero-dimensional linear crossing Weyl nodal objects have one upper limit is still an open question. In this work, combining angle-resolved photoemission spectroscopy with density-functional theory calculations, we show that the chiral crystal AlPt hosts a cube-shaped charged WNS which is formed by the linear crossings of two singly degenerate bands. Different from conventional Weyl nodes, the cube-shaped nodal surface in AlPt is enforced by nonsymmorphic chiral symmetries and time-reversal symmetry rather than accidental band crossings, and it possesses a giant Chern number |C|=26. Moreover, our results and analysis prove that there is no upper limit for the Chern numbers of such kind of 2D Weyl nodal object.