Extreme pressure conditions reveal fundamental insights into the physical properties of elemental metals that are otherwise not evident under ambient conditions. Herein, we use the density functional perturbation theory to demonstrate that the change in thermal conductivity as a result of large hydrostatic pressures at room temperature for aluminum is the largest of any known material. More specifically, in comparison to ambient conditions, we find that the change in thermal conductivity for aluminum is greater than the relative changes in thermal conductivities of diamond and cubic boron nitride combined, which are two of the most thermally conductive bulk materials known to date. We attribute this to the relatively larger increase in mean free paths and lifetimes of electrons in aluminum as a result of weaker electron-phonon coupling at higher pressures. Our work reveals direct insights into the exceptional electronic transport properties of pressurized aluminum and advances a broad paradigm for understanding thermal transport in metals under extreme pressure.