Chapman was born at Hitchin in Hertfordshire. He studied at Oxford but didn't take a degree. His earliest published works were the obscure philosophical poems The Shadow of Night (1593) and Ovid's Banquet of Sense (1595).
By the end of the 1590s he had become a successful playwright, working for Philip Henslowe and later for the Children of the Chapel. Among his comedies are An Humorous Day's Mirth (1597), All Fools (1599), Monsieur d'Olive (1606), The Gentleman Usher (1606) and May Day (1611).
His greatest tragedies took their subject matter from recent French history, the French ambassador taking offence on at least one occasion. These include Bussy D'Ambois (1607), The Conspiracy and Tragedy of Charles, Duke of Byron (1608), The Revenge of Bussy D'Ambois (1613) and The Tragedy of Chabot (published 1639).
Other poems include, De Guiana, Carmen Epicum (1596), on the exploits of Sir Walter Raleigh, a continuation of Christopher Marlowe's unfinished Hero and Leander (1598), and Euthymiae Raptus; or the Tears of Peace (1609). Some have considered Chapman to be the "rival poet" of Shakespeare's Sonnets.
From 1598 he published his translation of the Iliad in instalments. In 1616 the complete Iliad and Odyssey appeared in The Whole Works of Homer, the first complete English translation. Idiosyncratic but containing passages of brilliance, Chapman's Homer was much admired by John Keats, but is now rarely read.
Chapman died in London, having lived his latter years in poverty.