What service that lets you create records/data into an immutable database storage system that cannot be deleted?
While the specifics will depend on the database system itself this could be handled with pretty much any of the RDBMS platforms out there.  Permissions will pretty much handle what you want.  The process that puts the data in would need to have insert permissions and all other access would be select only.

As far as tracking the modifications - most of the vendors have some sort of auditing capabilities.  I am most familiar with Oracle and in that you can audit the activity of a user, activity on a specific table, or even any time a specific data modification statement (insert, update, delete) is executed.  Again this is vendor and version specific.

As a further protection - make sure to have good backups that can be used to restore to a specific point in time.  This will ensure that you can return the data to a specific state in case of an error or system failure of some type.