The ever-growing demand for faster and more efficient data transfer and processing has brought optical computation strategies to the forefront of research in next-generation computing. Here, we report a universal computing approach with the chirality degree of freedom. By exploiting the crystal symmetry-enabled well-known chiral selection rules, we demonstrate the viability of the concept in bulk silica crystals and atomically thin semiconductors and create ultrafast (<100-fs) all-optical chirality logic gates (XNOR, NOR, AND, XOR, OR, and NAND) and a half adder. We also validate the unique advantages of chirality gates by realizing multiple gates with simultaneous operation in a single device and electrical control. Our first demonstrations of logic gates using chiral selection rules suggest that optical chirality could provide a powerful degree of freedom for future optical computing.