You could either use a microcontroller or build a circuit like this
. The latter uses 10 leds, each lit in sequence. You can modify the circuit to use only 3 or 4 sets of LEDs and then have it reset the sequence (so the sequence would be 1, 2, 3, 4, 1, 2, 3, 4, 1...). The microcontroller can be programmed to create the same sequence or any that you want. Either way, you'll probably need to use a driver chip capable delivering the current to the LEDs. (The LED's would be setup in parallel sets like the chasing christmas lights). Just my $0.02.