Why did my chain start coming off on the right side of the chainring sometimes when I am pedaling in high gear?
Chains life spans have huge differences, depending on both conditions and maintenance and quality of the chain itself. If you have 2000 miles on the chain and it has been exposed to road salt, it is very likely that it has been worn out. If you are lucky, you can fix it by just replacing the chain, but if the chain is badly worn you may have replace the cassette and at worst case the chainring too. 

If you have to replace the chain ring, there are so-called narrow-wide chainrings that are designed to hold the chain better in single chainring setups.