Maybe you could just count how many charts are on that worksheet (is the chart
on a worksheet???).

If there's one, then you're done and get out?

Option Explicit
Sub auto_Open()

   With Worksheets("sheet1") '<-- change this
       If .ChartObjects.Count > 0 Then
           Exit Sub
       End If
   End With
   
   'code to make the chart
End Sub

You could look for the chart name, too.

Option Explicit
Sub auto_Open()
   Dim TestChartObj As ChartObject

   With Worksheets("sheet1") '<-- change this
       Set TestChartObj = Nothing
       On Error Resume Next
       Set TestChartObj = .ChartObjects("Chart 1")
       On Error GoTo 0
       
       If TestChartObj Is Nothing Then
           'create the chart
           MsgBox "create the chart here"
       End If
   End With
End Sub

If you ctrl-click on the chart, you can see the chartobject's name in the
namebox (to the left of the name box).

Code your auto_open so's it looks for a flag in a cell.

The flag can be anything like a text string.........."qwerty"

If this flag is present, the auto-open will stop.

Private Sub Auto_Open()
       If Sheets("Sheet1").Range("a1").Value <> "qwerty" Then Exit Sub
       MsgBox "do the stuff"
End Sub

Gord Dibben  MS Excel MVP