Chat support will most likely be offered for Mac and iOS devices as Apple needs to utilize customer support as it faces increase competition from other companies like Samsung. 24/7 Phone support could be considered in the future if the web chat support is successful.
In addition to 24/7 support, Apple is also planning on rolling out a revamped AppleCare website featuring an iOS-style interface with easy to understand controls. The new interface is focused on quickly connecting a customer to AppleCare while the current/previous versions focus on providing customers with support articles before connecting to an employee.
The new interface will reportedly be rolling out in the next few weeks...