Avoided level crossing muon spin resonance (ALC-μSR) spectroscopy was used to study radicals produced by the addition of the light hydrogen isotope muonium (Mu) to the discotic liquid crystal (DLC) 2,3,6,7,10,11-hexahexylthiotriphenylene (HHTT). Mu adds to the secondary carbon atoms of HHTT to produce a substituted cyclohexadienyl radical, whose identity was confirmed by comparing the measured hyperfine coupling constants with values obtained from DFT calculations. ALC-μSR spectra were obtained in the isotropic (I), hexagonal columnar (Col(h)), helical (H), and crystalline (Cr) phases. In the I and Col(h) phases the radicals, which are incorporated within the stacks of HHTT molecules as isolated paramagnetic defects, undergo extremely rapid electron spin relaxation, on the order of a hundredfold faster than in the H or Cr phases. The electron spin relaxation rate increases significantly with increasing temperature and appears to be caused by the liquidlike motion within the columns, which modulates the overlap between the π system of the radical and the π systems of the neighboring HHTT molecules, and hence, the hyperfine coupling constants. Rapid electron spin relaxation should occur for any π radical incorporated within the columns of a DLC, which may limit the utility of DLCs for future spin-based technologies.