Or get the parts to make a standalone arduino - buy an atemega that has a bootloader on, and these parts from dipmicro: 16 mhzcrystal, two 22 pf Capacitors, three 100nf capacitors, a 10K resistor, a 28 pin socket, and some perfboard to build it up on.
And a 5V wallwart for power.
Program your new chip with your sketch using your arduinio, confirm it works, then plop it into your new board.
Wire it up like so with your parts going go to where I show connectors.
Should end up looking like the little green board here, with connectors as you need for your parts.
This one has I think a 10-pin connector - +5 in (from the PCB on the left), +5v out (to the PCB on the right), ground (from the PCB on the left), serial in (from the PCB on the left) and 3 output lines to each PCB.