Chetham was born in Crumpsall, Lancashire, England, the son of Henry Chetham, a successful Manchester merchant who lived in Crumpsall Hall. He was educated at Manchester Grammar School, and in 1597 was apprenticed to Samuel Tipping, a Manchester linen draper. Chetham remained with Tipping until 1605, when he moved to London with his brother George and set up a partnership with him trading in various textiles. The business was successful, since the fabric was bought in London and sold for a higher price in Manchester. He acquired Clayton Hall in Manchester as his home, and in 1628 was also able to buy Turton Tower from William Orrell.
In 1631, he was asked to be knighted after his huge wealth became known to the crown, but he refused it, and so was fined. He later became the High Sheriff of Lancashire in 1635, a job he was unable to refuse, and in 1643 he was forced into the position of General Treasurer of Lancashire, which he found very difficult for his age. He also began to obtain debts, and he feared that on his death parliament would take his money. He therefore donated money to form a blue coat school for forty poor boys, which later became Chetham's Hospital and then Chetham's School of Music. He also left money to form the Chetham's Library, which included money to pay for the books. More libraries were constructed later on from this money.
After Chetham's death, at Clayton Hall, in 1653, the school and library opened. His contribution is commemorated by a statue and a window in Manchester Cathedral and by a statue and mural in Manchester Town Hall. By prior arrangement, Clayton Hall was left to the surviving nephew, George.