We have successfully synthesized the new S = 1/2 anisotropic kagome antiferromagnet ZnCu3(OH)6SO4 and determined its structure by synchrotron x-ray diffraction. No magnetic ordering is observed down to 50 mK, despite a moderately high Weiss temperature of Θw ∼ −79 K, indicating that the compound is a new quantum spin liquid (QSL) candidate. A linear temperature dependence of the magnetic heat capacity is found at 6 ∼ 15 K and below 0.6 K. Temperature-independent intrinsic susceptibilities are observed exactly in both temperature ranges. This consistently suggests a gapless QSL below 0.6 K, which may evolve from an unconventional quantum spin state at higher temperatures (6 ∼ 15 K).