Chipp was born in London in 1793, joining the choir of Westminster Abbey where he was taught the piano by Muzio Clementi. However, it was on the harp where he distinguished himself, writing many popular pieces, as well as longer compositions for other instruments including a trio for violin, viola, and cello (c.1820), a string quintet in E minor (1836), and a string quartet (1845).
For over fifty years Chipp played in all the principal London orchestras, at three coronations (George IV, William IV, and Victoria) and at all the principal festivals. His last public appearance was in 1866 at the Worcester Festival. He died on 19 June 1870 in Camden Town, leaving two sons, Edmund, a composer and organist, and Horatio, a cellist. He was buried on the western side of Highgate Cemetery.
