Cumulative Upkeep on the Stack
No, not quite. The age counter isn't actually placed on Glacial Chasm until the cumulative upkeep trigger resolves. When it resolves, as part of the same triggered ability, you must then pay two life for that counter or sacrifice Chasm. You can't remove the counter before you have to pay two life for it because you don't get priority while an ability is resolving. 

You can, however, remove each counter immediately after the cumulative upkeep trigger resolves, meaning you pay only pay two life per turn indefinitely.