Cataclysmic variables (CVs) are binary systems consisting of a white dwarf (WD) accreting matter from a companion star. Observations of CVs provide an opportunity to learn about accretion discs, the physics of compact objects, classical novae, and the evolution of the binary and the WD that may ultimately end in a Type Ia supernova (SN). As Type Ia SNe involve a WD reaching the Chandrasekhar limit or merging WDs, WD mass measurements are particularly important for elucidating the path from CV to Type Ia SN. For intermediate polar (IP) type CVs, the WD mass is related to the bremsstrahlung temperature of material in the accretion column, which typically peaks at X-ray energies. Thus, the IPs with the strongest hard X-ray emission, such as those discovered by the INTEGRAL satellite, are expected to have the highest masses. Here, we report on XMM–Newton, Nuclear Spectroscopic Telescope Array (NuSTAR), and optical observations of IGR J15038−6021. We find an X-ray periodicity of 1678 ± 2 s, which we interpret as the WD spin period. From fitting the 0.3–79 keV spectrum with a model that uses the relationship between the WD mass and the post-shock temperature, we measure a WD mass of |$1.36^{+0.04}_{-0.11}$| M_⊙. This follows an earlier study of IGR J14091−6108, which also has a WD with a mass approaching the Chandrasekhar limit. We demonstrate that these are both outliers among IPs in having massive WDs and discuss the results in the context of WD mass studies as well as the implications for WD mass evolution.