Not mandatory, but extremely helpful. It takes me about 45 minutes to cool 5 gallons of boiling wort to 70 degrees in my bathtub. Of course, I have very cold well water (approx 45 degrees in the winter). I have sped up the process by putting a frozen 2 liter soda bottle directly into the wort, but all the crackling scared the hell out of me. Thought the whole bottle might break and then I'd have 2 liters of unsanitized water in my wort. A chiller is very high on my wish list.
BTW, the reason Papazian doesn't mention cooling when talking about extract is because he's doing concentrated boils and dumping it into a fermentor of cold water. That'll cool your wort pretty quickly.