The Park chain checker is not very accurate... I prefer a ruler and when a chain has stretched to 12 1/16 I install a new one and for me this is usually after 4000 km / 2500 miles.

If you have ridden 3000 miles on a bike that was already used I would be quite sure the chain is worn significantly but because the chain, chain rings, and cogs wear together it may still run smoothly.

If you replaced the chain and left the other components you might experience drive train issues such as skipping gears as the new chain may not mate with what could be a rather worn cassette.

Experience has shown that a chain should last at least 2000 and a cassette should last 2- 3 times that if the chain is replaced before it exceeds an acceptable wear limit of 1/16 over... chain rings will last much longer than this depending on their quality as they do not experience as much load as the smaller drive cogs.