chair (n.)
early 13c., chaere, from Old French chaiere "chair, seat, throne" (12c.; Modern French chaire "pulpit, throne;" the more modest sense having gone since 16c. with variant form chaise), from Latin cathedra "seat" (see cathedral).

Figurative sense of "authority" was in Middle English, of bishops and professors. Meaning "office of a professor" (1816) is extended from the seat from which a professor lectures (mid-15c.). Meaning "seat of a person presiding at meeting" is from 1640s. As short for electric chair from 1900.
chair (v.)
mid-15c., "install in a chair or seat" (implied in chairing), from chair (n.); meaning "preside over" (a meeting, etc.) is attested by 1921. Related: Chaired.