How do you make the chooser card random? Do you pick out the treasure cards from your deck and then shuffle?
If we assume that the order of cards in your discard doesn't matter, then sure. I know that
Dominion generally doesn't allow players to search through their discard piles, but that seems like a rule that can be broken without a tremendous amount of harm, at least in this small capacity. You'd have to clarify in the rules section of this card that the choice has to be made before a player can look through their discard pile. Admittedly, I forgot you couldn't look through it when I designed this card; we played for months allowing such looking before someone read that you can't.
I suppose the process gets rather overwhelming the bigger your discard pile gets. I overlooked that. I could change it to an open decision, or make it top-most. The latter has the ugly problem of players having to keep their discard pile organized at all times.