Actually, AceCalhoon is only correct for the most part. While the counter-spell can be blocked with another counter-spell, a single wizard could not counteract the counterspell that attacks the spell it is casting. Although he can react, he can not throw counterspell in the middle of singing a fireball.
Magician One tries to throw fireball.
The player's assistant uses counterspell.
The Magician One can not counteract again because he is in the middle of throwing a fireball.
Both fireball and counterspell have verbal components. According to the rules of the components in PHB 203, "If you can not provide one or more of the components of a spell, you can not cast the spell."
You need multiple assistants for this, or a sorcerer with a subtle Metamagic spell