How to assign a class ID at runtime?

I'm working on runtime scripting and I feel like I am very close.

Using the C# evaluator I am able to create a class at run time that inherits from MonoBehaviour.

However when I try to assign it as a component I get the error "Invalid class ID = -1".

I assume Unity is keeping an internal table that maps classes to IDs for serialization purposes.

Can I add my class to that table in some way?