Your Chief can also:
collect firewood & dry grass, heal people, and put water on the firepit. Probably s/he can also collect flowers for potions, but I haven't actually tried that.

As far as the Chief directing work, I've had limited success with that. Since my villagers never seem to want to build that third hut (!!), I usually have my Chief directing their efforts. Sometimes it even helps, but I've come back to the game on occasion to find that the Chief is the only one still there!! Everyone else has run off to go fishing, or swimming, or "enjoying the bath", or whatever.