Paying 3 for Chalice

[KillemallCFH]

I was playing a game on MWS a few days ago and my opponent had a Chalice at 2 (and no Trinispheres), and then proceeded to pay 3 mana to play a Chalice at 1 (so that it wasn't countered by Chalice at 2). I really don't think this works, but I didn't care enough to argue at the time. Am I correct, or does this actually work? If so, why?

[Osse]

Without all the rules, the short story is that it doesn't work. the cost is XX, and if you make X=1, then both 'X's will be 1. so paying 3 doesn't work, as you can't make X=1.5

[KillemallCFH]

Oh, sorry. I must be tired or something.

No, you declare the value of x and then pay X+X. No more, no lessAlright, thanks. That's what I thought, I was just too lazy to argue it.