I like what Ripjiggen said about putting a insert in it. The inserts they make now are more efficient and some have fans built in to reclaim some of the heat going up the chimney. I also have have noticed that when I first start a fire it sometimes smoke a lot at the start, so I open a outside door to even the pressure in the house until there is a good flame that warms up the chimney and creates a good draw. (The smoking should stop right away once the pressure is released).
You need to get the chimney warmed up fast to create that draw ( I like to use newspapers or small kindling to do this.
If that does not work see if you can extend the chimney height above the the roof more to get more draw.