A formula will do this for you, ie: =IF(B3="",B3,"")
Place formula in cell C3 and copy down.
If you must use VBA, the try this:
Sub CopyVals()
Dim intLastRow As Integer
intLastRow = ActiveSheet.Range("A65536").End(xlUp).Row
For Each c In Range("A1:A" & intLastRow)
If c.Value <> "" Then
c.Offset(0, 1).Value = c.Value
End If
Next c
End Sub