Rate coefficients have been measured for the H + HC3N (cyanoacetylene) reaction at T = 200, 250, and 298 K and at P = 0.5, 1.0, and 2.0 Torr He using a discharge-flow mass spectrometry apparatus. The reaction was monitored under pseudo-first-order conditions with the H atom concentration in large excess over the HC3N concentration ([H]/[HC3N] = 100-665). H atoms were generated by the fast reaction F + H-2 --> H + HF or by microwave discharge in H2. Fluorine atoms were produced by microwave discharge in an approximately 5% mixture of F-2 in He. Low-energy (24 eV) electron-impact mass spectrometry was used to monitor the HC3N decay kinetics to obtain the bimolecular rate coefficients. At T = 298 K the rate coefficients were found to be pressure independent over the range of pressures studied with an average value k = (2.1 +/- 0.3) x 10(-13) cm(3) molecule(-1) s(-1). This implies that the high-pressure limit is reached in these experiments not only at T = 298 K but also at the two lower temperatures. The temperature dependence of the measured high-pressure limiting rate coefficients is given by the following Arrhenius expression: k = (1.1 +/- 0.1) x 10(-12) exp[-(500 +/- 14)K/T] cm(3) molecule(-1) s(-1). A transition state theory model using G2M or CCSD(T) energies and Eckart tunneling corrections has been employed to calculate high-pressure limiting rate coefficients for this reaction. The reaction's mechanism and implications to the atmospheric chemistry of Titan are discussed.