Cleaning the soot from the exterior of your chimney is essentially not much different from cleaning your indoor brick. However, you will probably need a lot more elbow grease since those bricks are also exposed to weather and the elements. Pick a clear day and get out your ladder--you should be able to finish this project in just a few hours.
Things You'll Need
Mild liquid soap
Mix up your first cleaning solution. Fill the bucket about 2/3 of the way full with hot water. Add 2 cups of white vinegar. This will create a serious cleaning solution that is entirely green and will lighten up the mortar while fighting soot stains.
Start scrubbing at the top of the chimney; otherwise, you will wash the soot and debris over the clean parts of the chimney below. Climb up your ladder with your bucket of cleaning solution. Scrub the chimney with the steel wool. This will not hurt the bricks, but it will start to remove built-up creosote and soot. This may take a while. Dip the steel wool into the cleaning mixture regularly, and make more if you notice that the water is too dirty to continue cleaning. Really tough stains may require a wire brush.
Hose down the chimney. You can let the vinegar solution sit on the bricks as you work your way down the chimney. However, when you are done you may wish to do a second cleaning with the bristle brush. Wash the entire chimney down with the hose, starting at the top as before.
Scrub the chimney with soap and water. Mix about 6 drops of mild detergent into hot water in the bucket. Then, use the bristle scrub brush to scrub down the entire chimney again from top to bottom. This will remove any remaining dirt that may have gotten knocked loose with the bristle brush but not been fully removed from the chimney.
Wash down the chimney one last time. Use a lot of water and the highest pressure on your sprayer. Once your chimney dries, you will clearly see the difference now that you have removed the soot from the exterior bricks.
There are a variety of chemicals that you can use as well on bricks, such as TSP and other cleaners. However, white vinegar is completely green, and the liquid soap will quickly dilute down to nothing with repeated rinsing. To bleach out mold, add a cup of bleach to your mix.
If the ladder is not perfectly stable, work with a partner who can hold it in place for you.