Okay. One more observation before I go out and buy a ruler (which I am surely going to) and measure my chainline. My cog has 16 teeth. I carefully watched where the tooth feel between the chain links. Standing at the rear of the bike with it upside down, I started with number one and watched as this tooth was a little to the right of center between the plates of that link. When I got back around to tooth number one again, it was now dead center between the plates of the link it now occupied. I think my chain is all screwy. I picked another tooth (tooth #5 to be exact) and watched it as I slowly spun the rear wheel. I noticed the same erratic behavior. I will definitely be getting a new chain, as well, but I will also still measure the chainline.
Ryan