This is one theory - 'green' and 'pale' were alternate meanings of the same Greek word. In the seventh century B.C., the poetess Sappho, used the word 'green' to describe the complexion of a stricken lover. The Greeks believed that jealousy was accompanied by an overproduction of bile, lending a pallid green cast to the victim.
Ovid, Chaucer, and Shakespeare followed suit, freely using 'green' to denote jealousy or envy. Perhaps the most famous such reference is Iago's speech in Act 3 of Othello:
O! beware my lord, of Jealousy;
It is the green-ey'd monster which doth mock
The meat it feeds on.
Although we are now more likely to ascribe the pallor of a friend to a questionable tuna fish salad sandwich rather than an emotional fit, 'green with envy' remains entrenched.