The China Jinping Underground Laboratory (CJPL), located $\sim 2,400$~m beneath Jinping Mountain, is one of the world’s deepest and largest ($\sim 300,000m^3$) underground facilities, hosting dark matter, nuclear astrophysics, and neutrino experiments. We report the first muon radiography (muography) conducted at this extraordinary depth. Cosmic muons detected by a one-ton prototype developed for the Jinping Neutrino Experiment were used to perform non-invasive subsurface density mapping over a 3~km lateral range. The 1.3~m diameter detector provides nearly isotropic acceptance and an angular resolution of $\sim {4.5}^{\circ }$. By correlating the predicted surface muon flux distributions with the underground measurements, we reconstruct a directional opacity map that constrains the density structure of the overburden and shows excellent agreement with satellite-derived terrain models. This work demonstrates the feasibility of muography at extreme depths with kilometer-scale overburden and establishes a robust methodology for future geophysical applications and large-scale facilities, such as the full Jinping Neutrino Experiment. Based on this validated overburden model, we further predict the total muon fluxes for the eight experimental halls in CJPL-II, providing essential input for their physics programs.