In that case you can do away with your "Chain" table completely by using just a reference to the child or parent in the Member table.
Do you know what the max chain length is likely to be? Will it be greater than 10?
If so the most efficient way to handle this will be to do it in php with multiple queries not in sql.
so you run the first query to get the top level parent (or bottom level child) and based on the result of that you run another query if there is another child in the chain other wise you stop, and so on. You can do this with a simple loop.
I can't come up with an easy way to achieve this n-level chain with a single select statement.
If you really want to try doing it this way you should post again with a subject something like - "N-level self reference" and post the data structure above and see if someone comes up with a better solution.
Sorry I can't be of more help 🙁