Deny self is the same word used for Peter denying the Lord.  As Peter denied any relationship that he had with Jesus and any claim Jesus had on him, then we too must look at self, remember the times it has led us astray and let us down, then deny self’s ultimate claim on us.  The One who died for us has prior, present and perpetual claim on us.  Deny all that conflicts with that, and you will discover a relationship that will keep you in the tough times. 

The Lord turned and looked at Peter. And Peter remembered the word of the Lord, how He had told him, “Before a rooster crows today, you will deny Me three times.” Luke 22:61 (NASB)