...and you don't have to climb up the tower to see them, they have their own webcam. http://www.rspb.org.uk/webcams/birdsofprey/chichester.aspx

Also,

"From Wednesday 13th April the RSPB will be based at the Cathedral for its Date with Nature project, offering visitors a rare chance to watch the birds at close range without disturbing them.  Visitors will be able to view images from the nest, and use binoculars and telescopes to watch the birds flying and perching on the pinnacles and turrets of the Cathedral.

At first, the project will be based at the Cloisters Café.  At the end of May, when the young start to learn to fly, the RSPB will move out to the Cathedral Green, in front of the Cathedral.  The project runs until 10th July, and entrance to the Cathedral and use of the viewing equipment are free of charge." Read more over at the Peregrines at Chichester Cathedral page on the Chichester Cathedral website and over at the RSPB A Date With Nature page.