Chain repeatedly tries to click into place without gear change While pedalling, every 10 seconds or so, the chain on my bike makes the sound it makes during a gear shift - it "clicks", as if it's clicking into place in the new gear. But there is no gear shift going on - it just skips periodically as I pedal. 

It feels as if I briefly lose control, so I'd like to fix this before the problem gets worse. What could be causing this?
Since this occurs every 10 seconds, this leads to believe that you have a frozen link in your chain or a defective link in your chain. 

If it were a cable or dérailleur adjustment, it would occur all the time while pedalling. The pause leads me to think that the chain is fine when continuing around the big sprockets in the front, but when it gets to the cassette and dérailleur, the size of the cogs and the angle at which the chain is being bent causes the stiff link to manifest itself. 

As something you can fix at home (in the event of a stiff link), lube the chain with any bicycle lube. 

If that doesn't help it, you probably have a defective link and the bicycle should be brought to the local bike shop. 

Best of luck!