No. Chalice will counter the actual spell upon complete announcement of the spell (when the copy is still unresolved on the stack), so by the time the copy resolves, the actual spell is already countered.
Dante
This is only partly correct. Chalice triggers when you announce the spell, and the trigger goes on the stack immediately after the spell does. However, Replicate is also a trigger, and also goes on the stack immediately after the spell. So, the copy being unresolved on the stack is entirely dependant on who controls the chalice, and if your opponent controls it, it also matters whose turn it is. The chalice countering the original spell, however, is always correct.
So, assuming your opponent controls the chalice, and it is your turn, the stack will look like this (with the top being what resolves first:
Chalice Trigger
Replicate
Shattering Spree
if it's their turn, it looks like this:
Replicate
Chalice Trigger
Shattering Spree
Sorry to be a stickler on this, I'm just trying to make the answer precise, and easy enough to understand at the same time.
