My bicycle is a 2012 Specialized Secteur. It has 6000 miles (10000 km), and I have never replaced the chain.
I recently began noticing that the chain always seems out of alignment with the rear cassette, no matter how finely I adjust the rear derailleur. This feeling only occurs in certain gears (the ones I tend to use the most). In these gears, the chain clicks softly. It is almost like it wants to skip off of the current cassette gear onto another. The feeling is similar to when the rear derailleur needs an adjustment because it is trying to set the chain between two gears on the cassette.
I know that when a chain is worn, it will "jump" gears because it has enough free play to prevent a proper mesh with the gears of the drivetrain. That led me to research when a chain should be replaced. To my horror, I realized that I had ridden the bike three times the recommended replacement interval. I have regularly cleaned the chain throughout its life and kept it lubricated.
I know that I must replace the chain, but before I do, I would like to know if it is possible that the rest of my drivetrain is salvageable. Should I replace the chain and see if the problem goes away? If not, should I follow with replacing the rear cassette, then if that also fails to fix the problem, the front chainrings? Or, is it possible that this symptom that I am experiencing is not related to the chain's wear at all?