Acts 10:38:
How God anointed Jesus of Nazareth with the Holy Ghost and with power: who went about doing good, and healing all that were oppressed of the devil; for God was with him.
Throughout the Bible, God had His chosen servants anointed with oil to set them apart for His service. This included prophets, priests, and kings. Jesus was all three. See Jesus Christ: Prophet, Priest, and King for more details.
But Jesus was not anointed with the traditional oil. His anointing was with the holy spirit. At his baptism by John, the spirit appeared like a dove—pure and simple. Isaiah had promised God’s coming savior would be anointed with His spirit in Isaiah 61:1. Jesus quoted that scripture when he opened his ministry in Nazareth.