There are a lot of mythological references, which states that the crow of a rooster is fatal to a Basilisk.
From CHAPTER XXXVI of the Bulfinch's mythology, MODERN MONSTERS- THE PHOENIX- BASILISK- UNICORN-SALAMANDER.
There is an old saying that “everything has its enemy” – and the cockatrice quailed before the weasel. The basilisk might look daggers, the weasel cared not, but advanced boldly to the conflict. When bitten, the weasel retired for a moment to eat some rue, which was the only plant the basilisks could not wither, returned with renewed strength and soundness to the charge, and never left the enemy till he was stretched dead on the plain. The monster, too, as if conscious of the irregular way in which he came into the world, was supposed to have a great antipathy to a cock; and well he might, for as soon as he heard the cock crow he expired.
And from the Aelian's characteristics of animals (mythology from the 2nd century):
With its crowing a cock scares a lion and is fatal to a basilisk.
In addition, there are a lot of instances where this is mentioned in the Wikipedia article too:
From Tales of Canterbury:
basilisks can be killed by hearing the crow of a rooster
From the Cantabrian mythology:
The weasel is the only animal that can face and even attack it. It can only be killed with the crowing of a rooster, so, until very recent times, travelers were carrying a rooster when they ventured into areas where it was said that the basilisks lived
So, why is it that a rooster can fell such a monstrous creature?
Is there any reason behind the formulation or origin of this?
Related question on SciFi.SE: Can the crow of a rooster petrify/kill a basilisk?