Asimov’s Guide to the Bible, pp. 536–7:

Cockatrice

In the description of the ideal Messianic kingdom, several ways of indicating the total absence of danger or harm are to be found. In each, the trick is to combine the utterly helpless with the completely harmful. The climax is reached when infants are mingled with serpents.

Isaiah 11:8. And the sucking child shall play on the hole of the asp, and the weaned child shall put his hand on the cockatrice’ den.

The two parts of the verse contain the parallelism that is the essence of Hebrew poetry, and it may be taken that the Hebrew words translated as "asp" and "cockatrice" both signify some venomous serpent. The asp is, indeed, a small poisonous snake found in Egypt. (Cleopatra was supposed to have committed suicide by allowing an asp to bite her.)

The cockatrice, however, is something else again. The word may have originated in medieval times as a form of "crocodile." The crocodile, like the serpent, is a deadly reptile. It might almost be viewed as a gigantic, thick snake, with stubby legs. To Europeans, unfamiliar with the crocodile except by distant report, the snaky aspects of the creature could easily become dominant.

Moreover, once "cockatrice" is formed from "crocodile," the first syllable is suggestive, and the fevered imagination develops the thought that the monster originates in a cock’s egg. This is itself a monstrous perversion of nature for, of course, cocks are male birds that do not lay eggs. The egg, thus perversely laid, must, moreover, be hatched by a serpent, and the product, then, is a creature with a snake’s body and a cock’s head.

The cockatrice is pictured as the ultimate snake. It kills not by a bite but merely by a look. Not merely its venom, but its very breath is fatal. Because the cockatrice is the most deadly snake and therefore the king of snakes, or because of the cock’s comb which may be pictured as a crown, the cockatrice is also called a "basilisk" (from Greek words meaning "little king").