Report is made of a systematic scaling study of the finite-temperature chiral phase transition of two-flavor QCD with the Kogut-Susskind quark action based on simulations on L3 × 4 (L=8, 12 and 16) lattices at the quark mass of mq = 0.075, 0.0375, 0.02 and 0.01. Our finite-size data show that a phase transition is absent for mq ≥ 0.02, and quite likely also at mq = 0.01. The scaling behavior of susceptibilities as a function of mq is consistent with a second-order transition at mq = 0. However, the exponents deviate from the O(2) or O(4) values theoretically expected.