From Google Maps: "Bethlehem is a Palestinian town south of
Jerusalem in the West Bank. The biblical birthplace of Jesus, it’s a
major Christian pilgrimage destination"
(probably taken from wiki but I didn't bother to dig deeper)
Discussion
When I went to Bethlehem some years back, yes, it was in the Palestinian-controlled territory. However, in Jesus' day it was in the Roman-controlled province of Judaea. And in the days of Jesus' ancestor Jacob, who buried his wife Rachel there, it was Canaanite-controlled territory.