A few drops of oil might change everything... often it will cure a mildly rusty chain immediately; sometimes it will make a skipping chain skip worse.
After the chain is oiled you can do a quick assessment by (1) turning the cranks backwards to see if it rides smoothly through the rear derailleur and over the cogs, (2) measure 12 pairs of links with an inch measuring tape - the distance from the centre of the first pin to the centre of the 25th pin should be between 12" and 12-1/16"... any longer and it is worn out and replacing it with a new chain will necessitate new cogs at least.