I've asked Donald whether Chameleon can override Enchantress like other Ways. (Yes, the rulebook doesn't say otherwise.)
We've had a long thread (about Lantern, Enchantress and Chameleon), and there are two ways of reading Chameleon. In both cases Chameleon triggers right when you're about to follow the instructions/ability on the played card.
1) Chameleon replaces the ability with itself (identical ability) and sets up future effects to happen whenever you get to resolving +$ and +Cards.
2) Chameleon replaces the ability with a modified version where all the +$ and +Cards that you would get this turn are already changed.
Chameleon seems to read like the first interpretation. That means you're set to follow the card's instructions when Enchantress tries to replace them, so that would seem to mean that Enchantress succeeds. But maybe the ruling could still be that Chameleon wins, maybe because Enchantress somehow "loses track" of an ability that has been removed and put back?
But, there's another interaction where it absolutely matters which timing Chameleon has: your -$1 token.
If it's the second interpretation, Militia gets changed to +2 Cards and you keep your -$1 token. If it's the first interpretation, Milita is still +$2, but when you would get those $2, you can choose which to resolve first: your -$1 token, or Chameleon's effect of giving you +Cards instead of +$. So you can either lose your token and get +1 Card, or keep your token and get +2 Cards.
Edit: GendoIkari has noted that it also applies to your -1 Card token.