The rapid growth of wearables has created a demand for lightweight, elastic and conformal energy harvesting and storage devices. The conducting polymer poly(3,4-ethylenedioxythiophene) has shown great promise for thermoelectric generators, however, the thick layers of pristine poly(3,4-ethylenedioxythiophene) required for effective energy harvesting are too hard and brittle for seamless integration into wearables. Poly(3,4-ethylenedioxythiophene)-elastomer composites have been developed to improve its mechanical properties, although so far without simultaneously achieving softness, high electrical conductivity, and stretchability. Here we report an aqueously processed poly(3,4-ethylenedioxythiophene)-polyurethane-ionic liquid composite, which combines high conductivity (>140 S cm-1) with superior stretchability (>600%), elasticity, and low Young's modulus (<7 MPa). The outstanding performance of this organic nanocomposite is the result of favorable percolation networks on the nano- and micro-scale and the plasticizing effect of the ionic liquid. The elastic thermoelectric material is implemented in the first reported intrinsically stretchable organic thermoelectric module.