The first scheme to enhance Eastgate came following the visit of the Prince of Wales to the city in 1869. In 1872 the local architect John Douglas was asked to prepare a number of designs by Hugh Grosvenor who was at that time the 3rd Marquess of Westminster. The Marquess offered to pay half the cost of the project but the Chester Improvement Committee would not allow any council funds for it, and the scheme came to nothing. The idea was revived to celebrate the diamond jubilee of Queen Victoria in 1896. At this time the 1st Duke of Westminster suggested that the city should support Queen Victoria's Jubilee Institute of Nurses. Other ideas suggested at the time were a statue of Queen Victoria in the Town Hall square, or a clock in the Town Hall tower.
A committee was set up and, despite early support for the Queen's Institute and for general festivities, it was finally decided to erect a memorial tower and clock on Eastgate. John Douglas prepared a new design which was approved in March 1898. The clock's faces and mechanism were paid for by Edward Evans-Lloyd, a local solicitor and freeman of the city, while the cost of the tower was financed by public subscription.
Source & More Information: Wikipedia, Eastgate and Eastgate Clock, http://en.wikipedia.org/wiki/Eastgate_and_Eastgate_Clock