Select DISTINCT records with extra information
SELECT c.*
FROM 
      Customers AS c
   INNER JOIN
      ( SELECT [Address 1], MIN([Order Date]) AS min_od
        FROM Customers
        GROUP BY [Address 1]
      ) AS grp
         ON  grp.[Address 1] = c.[Address 1]
         AND grp.min_od = c.[Order Date] ;


This may still give you two rows for an address, if you have two rows with the same minimum [Order Date] for an address.