The Kroll-Lee-Zumino renormalizable Abelian quantum field theory of pions and a massive rho-meson is used to calculate the scalar radius of the pion at next-to-leading (one-loop) order in perturbation theory. Because of renormalizability, this determination involves no free parameters. The result is < r(pi)(2)>(s) = 0.40 fm(2). This value gives for (l) over bar (4), the low energy constant of chiral perturbation theory, (l) over bar (4) = 3.4, and F-pi/F = 1.05, where F is the pion decay constant in the chiral limit. Given the level of accuracy in the masses and the rho pi pi coupling, the only sizable uncertainty in this result is due to the (uncalculated) next-to-next-to-leading order contribution.