3 Way flip flop between LEDs with 555 timer
A very common way to do what you want is to have one 555 acting as the oscillator, and drive a CD4017 Johnson counter with it.  The counter steps through 10 outputs in series, and you can make a connection such that after three steps it repeats.  You will need one driver transistor per LED because the 4017 output is pretty weak.

This type of circuit is called a chaser, and there are many example schematics on the web.