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We are building a chart with a rolling 12 month value. Our issue is that our data starts in Jan 2011 so the 1st month that would actually show a full rolling 12 months would be Jan 2012. We would like our graph to start showing data in Jan 2012 and graphically ignore data before Jan 2012 as it would be incomplete.

Try this:
Create an expression that put the months and years in order. On the picture examples I used the fiscal month (13, 14) and the month in a expression like this: "=FY*100 + Num(Month)" (So I have 1301, 1302, 1303, ..., 1401, 1402...).
You MUST to put this expression as the first expression, because the Dimension Limits will filter by the first expression.
Set the conditional flag and fill with "0" to this expression don't appears in the graph.

Then, on Dimension Limit (I don't know very well if this tab has this name in the English verson from Qlikview, but it might be something like this), you set the flag to limit the values of the first expression. Then you set the numbers of months that you want to appear on chart.

At the end I have this result. I don't have 36 months on my database, but I tested with less values and worked here.

You can see parameter in the next picture:

Regards,
Venelin