From what I gather, it is an 1GHz processor based on an improved ARM Cortex A8 architechture; however it is underclocked to 800MHz for battery life and thermal reasons. The chipset also includes a PowerVR SGX 535 GPU.
Reading around, it seems the CPU design is basically the same as the Samsung Hummingbird CPU found in the Galaxy S series. Apparently, the A4 is actually manufactured by Samsung, as well.