Steven,
This could be done automatically with VBA code, but can also be done using filters. Put a filter on the column of data that contains the date (you will need an Advanced filter) that filters the column for dates > Today - 365 (i.e., dates since one year ago). Since filtered rows (and columns) do not appear on graphs, this should do the trick. You just need to make sure the series on the chart includes the entire range of rows that you expect to contain data you want to plot even as you add data. This means that initially you will have to declare a range that goes well beyond the range of data currently on the sheet.
Happy charting.
Damon