Verified Answer :

Nekoneko

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.

derequinho

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)

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