The transverse-longitudinal asymmetry ATL′ in 3He⃗(e⃗, e′) quasielastic scattering at momentum transfer Q2=0.14 (GeV/c)2 has been measured to be 1.52 ± 0.55(stat) ± 0.15(syst)%. The plane wave impulse approximation (PWIA) prediction for this measurement ranges from 2.1% to 2.9%, where the variation is due to uncertainty in the initial state wave function, nucleon form factors, and off-shell prescription. The data may suggest a suppression with respect to the PWIA, which has also been observed for the unpolarized longitudinal response function.