By two different methods, we show that LHS 4033 is an extremely massive white dwarf near its likely upper mass limit for destruction by unstable electron captures. From the accurate trigonometric parallax reported herein, the effective temperature (Teff=10,900 K) and the stellar radius (R=0.00368 Rsolar) are directly determined from the broadband spectral energy distribution-the parallax method. The effective temperature and surface gravity are also estimated independently from the simultaneous fitting of the observed Balmer line profiles with those predicted from pure-hydrogen model atmospheres-the spectroscopic method (Teff=10,760 K, logg=9.46). The mass of LHS 4033 is then inferred from theoretical mass-radius relations appropriate for white dwarfs. The parallax method yields a mass estimate of 1.310-1.330 Msolar for interior compositions ranging from pure magnesium to pure carbon, respectively, while the spectroscopic method yields an estimate of 1.318-1.335 Msolar for the same core compositions. This star is the most massive white dwarf for which a robust comparison of the two techniques has been made.