What database to use to store action log?

I am building a game and want to store log of all actions in the game.

Requirements:

1. Each time action is taken it is appended to the log immediately
2. No queries are made on the logs. Only the whole log is retrieved when the game is loaded.
3. No data loss. Actions must never roll back

So, the most obvious way is to store the log in filesystem without any database. But when it comes to PaaS such as Heroku the filesystem is not a good way to operate there. So I need some simple datastore which acts as filesystem.