Question

Nancy thinks that she is a better chess player than
I
Me
Myself

Answer 1

Nancy thinks that she is a better chess player than me (coloquial)
Nancy thinks that she is a better chess player than I am (classical)

Answer 2

Nancy thinks that she is better chess player than me.

Myself is doing something alone. I made the doll by myself.
I is used by an action you made or discribing yourself. I am tall. I worked alone.
Me is used to mention yourself. Natalie was playing with me.