Web chat is a great channel alternative to offer your customers. If your "callers" happen to be in front of their computer and they are reasonable typists, web chat can be a very efficient way to complete a transaction. Depending on the chat technology, you can even lock down chat access behind a secure website to make it a very safe way to exchange potentially sensitive information.
The contact center can possibly gain efficiencies by enabling agents to handle multiple chat sessions simultaneously. (Be careful with this, though, as the complexity of an interaction and the responsiveness of the customer can result in a poor user experience if not balanced judiciously.) While long-distance charges are obviously avoided, it's not uncommon for average session durations to be longer for chat than for voice. The agent cost becomes even more critical for chat sessions.
At the end of the day, though, it's about fostering a great relationship with the customer. Tools and technology help to provide the best experience to the customer as efficiently as possible. The decision to offer chat should be more about the customer than about the business. I like to have a chat option when it suits my needs, but I find it very frustrating when chat is my ONLY option.