The reaction of CN radicals with HC3N is of interest for interstellar and circumstellar chemistry as well as for the chemistry of Titan's atmosphere, as part of a general scheme for cyanopolyyne synthesis within these low temperature environments. Here, we present the first experimental measurements of its rate coefficient below room temperature down to 22 K, employing the CRESU (Cinétique de Réaction en Ecoulement Supersonique Uniforme or Reaction Kinetics in Uniform Supersonic Flow) technique coupled with pulsed laser photolysis-laser-induced fluorescence. A novel pulsed version of the CRESU technique employing a new spinning disk valve was used for some of the kinetics measurements. The measurements were in excellent agreement with the only previous determination at room temperature and show a marked increase in the rate coefficient as the temperature is lowered, with the results being well represented by the equation k(T) = 1.79 × 10(-11)(T/300 K)(-0.67) cm(3) molecule(-1) s(-1), with a root-mean-square (statistical) error of 0.61 × 10(-11) cm(3) molecule(-1) s(-1), to which should be added 10% estimated likely systematic error. High accuracy ab initio quantum chemical calculations coupled with variational two-transition state theory calculations were also performed and demonstrate excellent agreement within the combined experimental and predicted theoretical uncertainties. The theoretical rate coefficients, adjusted within expected uncertainties, can be accurately reproduced over the 5 to 400 K temperature range by the expression [(1.97 × 10(-8)) T (-1.51) exp(-3.24/T) + (4.85 × 10(-13)) T (0.563) exp (17.6/T)] cm(3) molecule(-1) s(-1), where T is in K. The new measurements are likely to be of interest to astrochemical and planetary atmospheric modelers.