Create the new sheet, then copy and paste the data range with the chart.
When pasting, if the new sheet is to the left of the original sheet, the chart data will remain linked to the original one. So, you can paste then move the sheet to the left.
I am almost sure that there is a bug report about that.
I can’t reproduce the problem if copying the whole sheet as described in my answer.
Tested with 7.1.8.1 and 7.3.2.2 on Windows 7.