I pulled out the pull chain right out of the unit. How do I repair it?

If the chain broke inside the switch it self you must replace the switch. If any of the chain shows outside the switch you can add a new chain with a connecting link.

Here are instructions:

Ceiling fan pull chain replacement and repair - Ceiling Fans N More

The chain pull came out of the unit, can it be repaired?

No, just install a new switch, as per the instructions above.