Wearable electronic devices that can be integrated seamlessly into clothing for monitoring and feedback need to be not only flexible, but also stretchable with low stiffness. Currently there are few solid electrolytes that are sufficiently stretchable for wearable electronic devices. Here we report stretchable solid electrolytes that can be elastically stretched more than 500% of their original length with ionic conductivities as high as 7 x 10(-5) S cm(-1) and tensile breaking strengths larger than 1.5 MPa. These solid electrolytes consist of poly(methyl methacrylate) chemical networks solvated by an electrochemically stable ionic liquid. A stretchable supercapacitor was demonstrated by coating a stretchable solid electrolyte with carbon nanotube electrodes.