Chirality is ubiquitous in nature, and populations of opposite chiralities are surprisingly asymmetric at fundamental levels(1,2). Examples range from parity violation in the subatomic weak force to homochirality in biomolecules. The ability to achieve chirality-selective synthesis (chiral induction) is of great importance in stereochemistry, molecular biology and pharmacology(2). In condensed matter physics, a crystalline electronic system is geometrically chiral when it lacks mirror planes, space-inversion centres or rotoinversion axes(1). Typically, geometrical chirality is predefined by the chiral lattice structure of a material, which is fixed on formation of the crystal. By contrast, in materials with gyrotropic order(3-6), electrons spontaneously organize themselves to exhibit macroscopic chirality in an originally achiral lattice. Although such order-which has been proposed as the quantum analogue of cholesteric liquid crystals-has attracted considerable interest(3-15), no clear observation or manipulation of gyrotropic order has been achieved so far. Here we report the realization of optical chiral induction and the observation of a gyrotropically ordered phase in the transition-metal dichalcogenide semimetal 1T-TiSe2. We show that shining mid-infrared circularly polarized light on 1T-TiSe2 while cooling it below the critical temperature leads to the preferential formation of one chiral domain. The chirality of this state is confirmed by the measurement of an out-of-plane circular photogalvanic current, the direction of which depends on the optical induction. Although the role of domain walls requires further investigation with local probes, the methodology demonstrated here can be applied to realize and control chiral electronic phases in other quantum materials(4,16). Optical chiral induction and spontaneous gyrotropic electronic order are realized in the transition-metal chalcogenide 1T-TiSe2 by using illumination with mid-infrared circularly polarized light and simultaneous cooling below the critical temperature.