AHSME 1979 Problem 23

The edges of a regular tetrahedron with vertices $A ,~ B,~ C$, and $D$ each have length one. Find the least possible distance between a pair of points $P$ and $Q$, where $P$ is on edge $AB$ and $Q$ is on edge $CD$.

$\textbf{(A) }\frac{1}{2} \textbf{(B) }\frac{3}{4} \textbf{(C) }\frac{\sqrt{2}}{2} \textbf{(D) }\frac{\sqrt{3}}{2} \textbf{(E) }\frac{\sqrt{3}}{3}$