This is a classic stiff link. The most common cause is dirt or rust because of a failure to lubricate properly. The photo seems to bear this out. Oil your chain (if you don't know what you should use, ask your local shop, or search the forum or internet for "chain lube" and prepare for lots of interesting reading). Once you've oiled the chain flex the link between your fingers until it moves fairly freely. You don't have to get it perfect, only so it runs fairly smoothly, it'll loosen the rest of the way as you ride the first 1/4 mile.