I am trying to add a new chart in a new worksheet in a protected workbook, but the "plus sign" to add a new sheet is grayed out, so I can't add the sheet.

Thanks for any help.

I mostly do as bellow:
It is possible to create a new sheet for you chart, if you first select the data range then go to insert chart. Select chart type then In the chart Options window select new worksheet.

Unprotect the sheet.