This is a rhetorical question — the implied answer is no one. No human being can claim a perfectly pure heart. This is not despair but honesty — it is the foundation of humility and our need for God's cleansing. It points forward to the Gospel: we need a Saviour because we cannot clean our own hearts.
Memory phrase: God cleans our hearts.
Talk about it: Why do we need God to help us with our heart?
Prayer: God, clean my heart. I cannot do it myself.