Chaplin was born and raised in Windsor, Berkshire, the son of Cynthia , a drama teacher, and Peter Greenwood, a civil engineer. He has two sisters, Sarah Greenwood and Rachel Greenwood, and one brother, Justin Greenwood. He took his stage name after his mother's maiden name. He attended the Princess Margaret Royal Free School. At the age of 17, he enrolled in the Guildhall School of Music and Drama.