Optical rotatory powers of chiral cocrystals formed from the achiral molecules tryptamine and 4-chiorobenzoic acid were determined by the HAUP (high accuracy universal polarimeter) method. These cocrystals belonged to space group P2(1)2(1)2(1), and their absolute configuration was confirmed by the Flack parameter. In the M-crystal, 2-fold helical arrangements are formed in a counterclockwise direction between the two components through the quaternary ammonium salt bridge, hydrogen bond, and the aromatic pi-pi interaction along the c axis, while clockwise helices alone exist in the P-crystal. Large rotatory powers p(3)(M) = -355 and p(3)(P) = +352 deg mm(-1) were obtained along the c axis in the M- and P-crystal, respectively, at 632.8 nm and 303 K. The magnitude was 10 to 100 times larger than those for ordinary organic crystals. Further, it was confirmed that the negative sign was induced by the counterclockwise helical structures and the positive sign by the clockwise helices. In contrast, the rotations along the a and b axis which are in perpendicular directions to the screw axis were p(1)(M) = +138, p(1)(P) = - 140 deg mm(-1), and p(2)(M) = -56, p(2)(P) = +58 deg mm(-1), much smaller than p(3)(M) and p(3)(P). The results revealed that the helically arranged aromatic pi electrons as well as the helical ionic and hydrogen bond networks in the crystal contributed to the enhancement of the magnitude of these rotations.