Yep. Which is why Herod had all the male children 2 and under killed. Being the king, it worried him a tad when the King Makers (magi) from the East showed up and asked "Where is he who has been born King of the Jews?"
Also, it's quite likely that, rather than a star, the "light" they followed was God's shekinah glory. Same thing that appeared as a pillar of fire by night when the Hebrews were wandering about in the desert, but probably not in pillar form.