Removing the tree stump by chemical means involves either introducing chemicals or fire into the equation. Chemicals might include synthetic or organic fertilizers which aid stump rotting.
Fire is the quickest way to chemically remove a stump, but it is not a safe method by any means and requires close monitoring in order to avoid the fire from spreading. A smoldering tree stump could take hours to burn off, and if your city does not allow open burning, removing a tree stump with fire would not be an option for you in the first place.
Using chemicals to break down the stump also poses a hazard because you must make sure the chemicals do not affect children and animals which could come in contact with the stump. The chemicals, over time, gradually break the stump down to the point where it is easier to break up into smaller pieces, but some might remain and require burning. Even after the process is complete, you may still have to contend with the chemicals left behind in the soil.
If you decide to rely on decomposition to gradually break down the stump, you’ll likely have a long time to wait. Although it is the most environmentally friendly method of tree stump removal, the rotting process for a tree stump to break down naturally can take years. To encourage the rotting process, holes are usually drilled into the stump and filled with fertilizer, compost, or manure. Repeated applications may be necessary in the long process of stump removal using this method.