Adjust the decimal timer to suit. The data written to column 6 is just to show speed of cycle.
[VBA]Sub DoTime()
Application.OnTime Now + 0.000008, "DoTime"
Cells(Rows.Count, 6).End(xlUp).Offset(1) = Range("A1")
If Cells(Rows.Count, 4).End(xlUp) <> Range("A1") Then
Cells(Rows.Count, 4).End(xlUp).Offset(1) = Range("A1")
Cells(Rows.Count, 4).End(xlUp).Offset(, 1) = Timer
End If
End Sub

[/VBA]