The prospect of electronic circuits that are stretchable and bendable promises tantalizing applications such as skin-like electronics, roll-up displays, conformable sensors and actuators, and lightweight solar cells. The preparation of highly conductive and highly extensible materials remains a challenge for mass production applications, such as free-standing films or printable composite inks. Here we present a nanocomposite material consisting of carbon nanotubes, ionic liquid, silver nanoparticles, and polystyrene- polyisoprene-polystyrene having a high electrical conductivity of 3700 S cm -1 that can be stretched to 288% without permanent damage. The material is prepared as a concentrated dispersion suitable for simple processing into free-standing films. For the unstrained state, the measured thermal conductivity for the electronically conducting elastomeric nanoparticle film is relatively high and shows a non-metallic temperature dependence consistent with phonon transport, while the temperature dependence of electrical resistivity is metallic. We connect an electric fan to a DC power supply using the films to demonstrate their utility as an elastomeric electronic interconnect. The huge strain sensitivity and the very low temperature coefficient of resistivity suggest their applicability as strain sensors, including those that operate directly to control motors and other devices.