I actually got that far using the macro-recorder in Excel. The following was the code given by the macro-recorder:
ActiveChart.SeriesCollection(1).XValues = _ "='Differentiated Fathers'!$C$2:$C$26"

I think I just don't know how to translate that.

I originally tried
$Chart->SeriesCollection($series)->{XValues} = $Range;
But that gave the following error:
Win32::OLE(0.1709) error 0x80020003: "Member not found"
in PROPERTYPUTREF "XValues" at ./PollenAVG.pl line 150

If I get rid of the curly braces:
$Chart->SeriesCollection($series)->XValues = $Range;
Can't modify non-lvalue subroutine call at ./PollenAVG.pl line 150.