I have two tables in SQL Server: Customer and Address
Customer Table:
CustomerID FirstName LastName
----------- ---------- -------
It is giving this row because you have AddressID in the select list for you subquery "P". So even though you don't have AddressID in you top level select this, the PIVOT function is still grouping by it. You need to change this to:
SELECT CustomerID, Firstname, Home as HomeCity, Office as OfficeCity
FROM ( SELECT C.CustomerID, C.FirstName, A.AddressType, A.City
FROM #Customer C, #Address A
WHERE C.CustomerID = A.CustomerID
) AS P
PIVOT
( MAX(city)
FOR AddressType in ([Home],[Office])
) AS PVT
Although I would be inclined to use an explicit INNER JOIN rather than an implicit join between customer and Address.