An exchange effect in one-dimensional quantum-wire electron-gas systems is investigated. The theoretical study presented shows that the electron population of a symmetrical structure consisting of two parallel quantum wires in close proximity may exhibit bistability with all electrons contained in one of the quantum wires. Compared to a similar effect in a two-dimensional system reported earlier, the excitation energy associated with the transfer of one electron is found to be much larger. For certain configurations, this energy can be as large as ∼50 meV. The theory predicts the exchange-induced bistability to exist in realistic configurations, and it may possibly be used in practical electronic devices such as memory elements.