754 - here's my 2c ... I had the exact problem. I bought my bike 2 years ago with around 8k miles and I doubt it had been cleaned in, oh, 32 years. I put the bike on the center stand and scrutinized the chain while I turned the wheel and could see there were a few links that were binding. I first confirmed the wheel was adjusted straight. I really didn't want to remove the swingarm to soak the chain in kerosene, so I took a scrub brush (the plastic kind you'd use on floors or kitchens with plastic bristles) and scrubbed the chain as I sprayed WD40 on it, and slowly turned the wheel. I probably used 1/2 bottle of WD40, but if very effectively cleaned the chain and removed the debris that was impairing the smooth movement of the chain. The tight...loose...tight cycle was eradicated. I bought a Castrol spray on lube from DennisKirk and have had no problems for two years now.
Hope this helps!