To find the least number of camp counselors needed, we first need to divide the 39 campers into groups of 6.
We can calculate the number of groups by dividing the total number of campers (39) by the number of campers per group (6):
\[ \text{Number of groups} = \frac{39}{6} = 6.5 \]
Since we cannot have a fraction of a group, we round up to the nearest whole number. This means we will have 7 groups.
Since each group requires 1 camp counselor, the total number of camp counselors needed will be equal to the number of groups.
Thus, the least number of camp counselors needed is:
\[ \boxed{7} \]