By high gears do you mean the two smallest? In the rear the smallest are the highest.
This problem would be typical for cogs that have been worn due to riding with a chain that has stretched too much causing uneven wear on the cog teeth. When replaced with a new chain the chain links do not mesh with the worn cogs. If that is the case you will need to replace the cassette or freewheel, whichever you have. You didn't give us a lot to go on. Have you measured the chain for stretch?

edit: Hillrider posted at the same time so I had not seen his post. I agree with his assessment.