I like the code from Jeeped, but it isn't the best readable one. Therefore, here is another solution.
Sub remDup()
Dim rng As Range, dupRng As Range, lastrow As Long, ws As Worksheet
Dim col As Long, offset As Long, found As Boolean
'Disable all the stuff that is slowing down
Application.ScreenUpdating = False
Application.EnableEvents = False
Application.Calculation = xlCalculationManual
'Define your worksheet here
Set ws = Worksheets(1)
'Define your column and row offset here
col = 3
offset = 0
'Find first empty row
Set rng = ws.Cells(offset + 1, col)
lastrow = rng.EntireColumn.Find( _
What:="", After:=ws.Cells(offset + 1, col)).Row - 1
'Loop through list
While (rng.Row < lastrow)
Do
Set dupRng = ws.Range(ws.Cells(rng.Row + 1, col), ws.Cells(lastrow, col)).Find( _
What:=rng, LookAt:=xlWhole)
If (Not (dupRng Is Nothing)) Then
dupRng.EntireRow.Delete
lastrow = lastrow - 1
found = True
If (lastrow = rng.Row) Then Exit Do
Else
Exit Do
End If
Loop
Set rng = rng.offset(1, 0)
'Delete current row
If (found) Then
rng.offset(-1, 0).EntireRow.Delete
lastrow = lastrow - 1
End If
found = False
Wend
'Enable stuff again
Application.ScreenUpdating = True
Application.EnableEvents = True
Application.Calculation = xlCalculationAutomatic
End Sub
It works with more than one duplicate and you can define an row offset, which defines how much rows you ignore at the beginning of the column.