Depends on your riding...
But to find out if yours is worn, take a ruler and put the "0" in the center of a chain rivet...the "12" should be on the rivet or within 1/16th of an inch. If it is over that, replace the chain.
Worn chains, seriously worn chains (over 1/16th) mean you also need to check the rear cassette for wear. Put a now chain on a worn casette and it will skip badly.
I can get about 2,000 miles out of a Dura Ace chain FWIW.
I use a Park Tool chain measuring tool. If it is worn, off the chain goes right away. I start checking at about 1,500 miles.