Experiments that measure the viscoelasticity of single molecules from the Brownian fluctuations of an atomic force microscope (AFM) have provided a new window onto their internal dynamics in an underlying conformational landscape. Here we develop and apply these methods to examine the internal friction of unfolded polypeptide chains at high stretch. The results reveal a power law dependence of internal friction with tension (exponent 1.3 +/- 0.5) and a relaxation time approximately independent of force. To explain these results we develop a frictional worm-like chain (FWLC) model based on the Rayleigh dissipation function of a stiff chain with dynamical resistance to local bending. We analyse the dissipation rate integrated over the chain length by its Fourier components to calculate an effective tension-dependent friction constant for the end-to-end vector of the chain. The result is an internal friction that increases as a power law with tension with an exponent 3/2, consistent with experiment. Extracting the intrinsic bending friction constant of the chain it is found to be approximately 7 orders of magnitude greater than expected from solvent friction alone; a possible explanation we offer is that the underlying energy landscape for bending amino acids and/or peptide bond is rough, consistent with recent results on both proteins and polysaccharides.