To find the coterminal angle, we need to add or subtract a multiple of $2\pi$. Let $x$ be the angle in radians that is coterminal with $3\pi$. Then we have the equation $x=3\pi+2\pi n$, where $n$ is an integer. To find the least positive angle, we want to find the smallest nonnegative value of $n$ that makes $x$ positive. Since $x$ is negative when $n=0$, we want to add the smallest positive multiple of $2\pi$ that makes $x$ positive. In other words, we want to find the smallest positive value of $n$ that makes $3\pi+2\pi n$ positive. The smallest positive value of $n$ that satisfies this condition is $n=1$, so the least positive coterminal angle to $3\pi$ is $x=3\pi+2\pi(1)=3\pi+2\pi=\boxed{5\pi}$.
