Is there an IC chip to toggle through three outputs?
You might want to try a 4017 (CMOS) or 74HC4017 (TTL) Johnson decade counter. (Philips 74HCT4017 @ Jameco).

You can wire the output of whatever number you want to reset at to the reset pin.

For example you would connect the pulse output of the 555 to pin 13 or 14 (depending on whether you want to trigger when the pulse is low or high), the LED's to the first 3 outputs (pins 3, 2, 4), and output 4 (pin 7) back to reset (15).