The thin-film dielectric response of organic films confined within a surface forces apparatus (SFA) and also between parallel sheets of atomically smooth mica is reported for the first time. Analysis is presented to infer dielectric properties of the organic film from the measured capacitance of the total system: sample, and mica sheets intervening between sample and electrodes. Measurements concerned the frequency dependence of normal-mode dielectric relaxation of cis-polyisoprene having dipoles aligned in the same direction along the chain backbone. We find that in thin-film geometries the peak frequency, f(peak), of normal mode dielectric loss (epsilon") is moderately lower than for bulk samples and that, more important, the expected terminal tail, observed in the bulk sample (epsilon"proportional to f for f < f(peak)), is not observed even at the lowest frequency examined. Thus the slow normal mode distribution is much broader and the terminal relaxation time is much longer for chains in the thin layers. These dielectric features are attributed to spatial constraints on global chain motion in the thin layers and also to adsorption of chains on mica surfaces when the layer thickness is comparable to the unperturbed chain dimension. Independent measurements of shear relaxation, performed using a SFA modified for measurement of dynamical mechanical shear rheology, found a tremendously retarded viscoelastic response relative to bulk samples. There is the possibility that the broad distribution of the dielectric response of individual polymer chains may correspond to the observed retarded viscoelastic relaxation. However, we cannot rule out the other possibility that the dielectrically detected relaxation of individual chains is still faster than the terminal viscoelastic relaxation and that the latter thus corresponds to the collective motion of many confined chains.