In my experience an 8 speed chain on a 9 speed triple crankset can cause issues with the chain hitting the chainring ramps. A compact double will likely not have the same problem and several here have posted about successfully using 8 speed chains on 9 speed cranksets. You can always try it and see if it works. If not, a new 9 speed chain can be had for ~$15 and will work fine with the rest of your components.