HERE is a You Tube vid where they show the different materials you can cut with Nesties. It does say lightweight Chipboard.
Here is a link to Sizzix, where it lists what Thinlits will cut. It does not mention chipboard at all.
Both these types of die are the wafer thin ones, which means I am pretty sure they will not cut anything thicker than heavy weight cardstock,or thin chipboard but I may be wrong. I think you would need the Steel Rule dies (like Bigz, for instance) for thicker chipboard.I'm sure someone will correct me if I am assuming wrong,
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HTH.