Measurements of the spin-dependent asymmetry in scattering longitudinally polarized electrons from polarized He3 at quasielastic kinematics are reported. The measurements were made at two kinematics and spin angles, one sensitive to the helicity-dependent transverse-longitudinal interference response function, RTL′, and the other to the helicity-dependent transverse response function, RT′. For the experiment a metastability exchange optically pumped polarized He3 target was used; a general discussion of the technique used to polarized the He3, along with the details of the design and operation of the target system, are presented here. A comparison is made of the world’s data on the He→3(e→,e′) quasielastic asymmetry with several theoretical predictions, including calculations that use the plane wave impulse approximation and a fully spin-dependent spectral function. There is good agreement between data and theory at the current level of experimental precision.