I have some tree stumps in my yard which make it difficult to mow - a task that I loath to begin with. Are there any chemicals that would speed their decomposition? Something that is environment friendly preferred.
Have you tried ammonium nitrate 
Couldnt resist.
I prefer the J.J. Walker method: Dy-no-mite!
The fastest, and possibly most expensive, is to rent a stump grinder. If you’ve never seen one, it’s an engine driven wheel with grinding teeth mounted on the rim. It’s spun by the engine and moved around until the stump is ground down below the ground surface. All that’s left is chips. These can be swept up and disposed of.
Last time I rented one it was about $80 for a day.
Depending of the stumps location, you may wish to try to burn the things using bbq bricketts. The bricketts can burn for a couple of days and can dry out and burn enough of the stump where you can more easily use a hand ax.
I think the local fire marshall might take issue with that approach.
When we built our home on what used to be the family farm they scraped the area for the house but we still had lots of stumps to remove.
My hubby and son soon discovered that the way to remove a stump was not to attack the stump itself but to excavate the soil around it until you exposed the large tap roots. Chop those with a mattock and then just pry the stump up with a spud bar.
I know this sounds labor intensive and it is but it is a lot easier than chopping at the stump.
Locally, on a lot a guy rented a small bulldozer with a digger arm for $250 per day & that was the fastest way of all.