I have to disagree with Bob, all H2S and other gases is/are caused by bacteria. They create gas in their digestion system as we all do. For H2S, it is sulfate reducing bacteria (SRB, mostly) BUT.. they live in the ground and groundwater, so the H2S can migrate to a well with the recovery water or be formed in the well by SRB, IRB (iron) and/or manganese (MRB) reducing bacteria. Each type is a group of bacteria. The groups can be made up of both aerobic and anaerobic types; needing oxygen or not.
As to the pellet droppers, there are a number of different brands and I sell them in certain cases like IRB shutting down a pump, or causing such rust that it blocks the drop pipe etc.. They can all cause serious damage if not set up correctly based on the water quality and how they are installed. All of them should insure that the pellets get down in the water that is usually done by including a piece of tubing down past any pitless or other obstructions. Always follow the manufacturers' instructions.
I wouldn't suggest BobNH's way due to too much owner involvement. Homeowners tend to skimp on doing what needs to be done when it needs to be done. Plus, in our rock wells, the water comes down from the static water level rather than up from the bottom of the well. In a cased/screened well, you'd need to put the chlorine at the screening with the largest flow if you held to the theory but, you have to chlorinate the whole column of water, not just what is going in to the pump inlet and there is a minimum contact time required for the chlorine to do it's job on iron, manganese bacteria gasses etc.. When you chlorinate in the well, we use the well as a retention tank. Usually the water will be very discolored if iron or IRB is present. And you don't want that stuff clogging up the drop pipe just moving through it up to the turbidity filter at the house that removes the 'dirt'. And the oxidation process has to be completed before the filter in most cases.
There is a knock off of the inline chlorinator I suggest. The one I sell is patented with a totally different inside workings than the knock off that is used for swimming pools.
A cold water odor of 'sulfur' says there is H2S in the water. Usually the hot water will smell too but the temp masks it. Yes Cass, there is a formula for chlorine demand; each ppm of iron, like 4 ppm of chlorine, H2S maybe 2-8 ppm etc.. I can never remamber it so I always follow the instructions wit hthe pellet dropper I sell. I don't shock wells anymore but used to use a 1/2 lb of pellets per 100' of water. You should find the info with a search for shocking + chart or some such. This will get you started:
http://www1.agric.gov.ab.ca/$department/deptdocs.nsf/all/wwg408?OpenDocument
Gary
Quality Water Associates