Chains should be replaced every 1500-2000 miles. They are narrow and do wear out quickly. If you let them go until you can tell that they need to be replaced, then you probably have to replace the cassette also. Cassettes cost $60-80 or more, chains cost $20-40, so you save money by replacing the chain early.
Oil is good, grease is better.
2007 Peter Mooney w/S&S couplers/Terry Butterfly
1993 Bridgestone MB-3/Avocet O2 Air 40W
1980 Columbus Frame with 1970 Campy parts
1954 Raleigh 3-speed/Brooks B72