The Palatine Chapel is located in the Royal Palace in street Piazza Indipendenza, 1 . It is impossible to miss this monumental building. From the central station in Palermo visitors may take the bus lines 109 and 234.
If you take 109 you should exit at the stop Piazza Indipendenza or if you take the bus 234 then the exit stop is Basile Re-Ruggero. Both of these stops are just few meters from the Royal Palace and the Palatine Chapel.