In the formula bar of an x-y chart, I entered:

=SERIES(,'Sheet1'!xData,'Sheet1'!yData,1)

I tried both with and without the single quotes around Sheet1 -- either way
I get an error message indicating the formula contains an invalid external
reference. How can I solve the problem?

It should be indicated:

1) xData and yData both contain an INDIRECT function whose text argument is
a relative reference, thus data depends on which is the active cell. (I
select a cell and recalculate in order to plot different sets of data).
2) This method of charting DID work for me before; something is a little
different about the way I'm doing it.
3) xData and yData DO presently return correct values when entered as
arguments in a cell (e.g., SUM(xData)).