Originally Posted by BobbyG

I'm no expert (as I often prove), but putting a new chain on old gears can cause slippage.

They say that gears and chains wear together. I had put new chains on my bike a dozen times over the years without any problems...
until last year. I broke a chain on my 1984 Nishiki International and put a new chain on and encountered major slippage. I used this as an excuse to get a new gear-set with lower gearing (that my 56-year-old knees had been begging for). New chain + new gears = smooth shifting.

The gears were only $24 with a $10 install charge by the bike shop.

And if the gears are worn enough to not work with a new chain, they are worn and should be replaced.

Again, I don't know for sure in your case, but this was my experience.