How can I find an AVR chip with built-in RF transceiver?
Atmel has dedicated single chip solutions for wireless communication based on the AVR ATmega series.

They also have other architectures (such as ARM), which can be found generally from their MCU Wireless Solutions page.

If you're looking for a 2.4 GHz breakout board (evaluation kit) you might be interested in something like the RZRAVEN.

(Other evaluation kits.)