Well creosote really only comes into play when you have poor air flow. It looks like the Big Chief doesn't have good flow at all since it has no exhaust or intake. This could also be leading to your problem with the white smoke. The wood chips are trying to burn, but don't have sufficient oxygen to do so. The blue smoke every one talks about is from a clean burning fire. To have that, you need a good flow of oxygen to the fire, or in this case, wood chips. In most pits, as long as you keep good air flow through the smoker, creosote shouldn't be an issue. Maybe look around on the web for mods to add at least an exhaust to your Chief.
18.5" OTS, 22.5" OTG, CB Silver(Rip), Vintage Coleman Bullet, Pit Barrel, UDS