oldcrank

I've had this happen. What worked (for me, at least) was to apply lateral presure on the newly connected link. Such as:

1. hold the chain with your hands wrapped around it, and both of your thumbs on each side of the newly inserted rivet. Now pull gently toward you with both hands, while at the same time, pressing away from you with your thumbs.

2. Do the same thing to the other side of the chain, only opposite in action: push AWAY from you with your hands, and press TOWARD you with your index fingers by the rivet.

Test the link to see how smooth the result is. If it's still tight, repeat both steps with just a little more pressure. Check again. The link should now have the same smooth motion as the others.