It really makes me wonder when people tell me that it's not possible, even for Christians, to have a pure heart. I'm thankful that Scripture disagrees with that notion. A pure heart is not only possible; it is expected.
Who shall ascend into the hill of the LORD? or who shall stand in his holy place? He who has clean hands and a pure heart; who has not lifted up his soul unto vanity, nor sworn deceitfully. He shall receive the blessing from the LORD, and righteousness from the God of his salvation. (Psalm 24:3-5)
It seems that without a pure heart, we have no access to God at all. This fact makes me so overwhelmingly thankful that God has provided the means to have purity of mind and heart. Without His saving grace and regenerating power, I would be lost forever!