Try pasting this into the code for the worksheet in question:
Private Sub Worksheet_Change(ByVal Target As Range)
If Not Intersect(Range("A1").Precedents, Target) Is Nothing Then
MsgBox "Something Preceding Range A1 was changed"
End If
End Sub

Charles

dumb and frustrated wrote:
Is there a way to kick off a macro if the value of a specific cell changes?
The tricky part is that this particular cell's is driven by a formula (in
other words, the user does not manually enter data in this cell).