203.3 - The converted mana cost of an object is a number equal to the total amount of mana in its mana cost, regardless of color. Some effects ask a player to pay mana equal to an object's converted mana cost; this is a generic mana cost-it may be paid with any combination of colored and/or colorless mana, regardless of the colors in the object's mana cost.
Example: A mana cost of 
{U} translates to a converted mana cost of 5. [CompRules 2003/07/01]
203.4 - Any additional cost listed in an object's rules text or imposed by an effect isn't part of the mana cost. (See Rule 409, "Playing Spells and Activated Abilities.") Such costs are paid at the same time as the spell's other costs. [CompRules 2003/07/01]
203.Ruling.1 - If a cost has an "X" in it, the mana cost equals the amount announced as part of playing the spell or ability while it is on the stack, but if the card in any other zone, X is treated as zero.
In play, Chalice's CMC is always 0.
On the stack, it's CMC is the amount paid for it.
Conclusion, mana draining a Chalice for 2 counters results in 4 mana during the drainer's next main phase.