If your data is unsorted:
If column A has the unique identifier:
enter this formula into row one in an available column, and drag down all of the rows:
=COUNTIF($A$1:A1,A1)
That will number each record (first occurance of a dupe will have a 1, second occurance will have a 2, and so on)
Copy all of the formulas that you just entered then Paste Special... Values
Now you can sort on that column and delete all rows that have a number greater than 1