Fuel-driven self-assembly of actin filaments and microtubules is a key component of cellular organization. Continuous energy supply maintains these transient biomolecular assemblies far from thermodynamic equilibrium, unlike typical synthetic systems that spontaneously assemble at thermodynamic equilibrium. Here, we report the transient self-assembly of synthetic molecules into active materials, driven by the consumption of a chemical fuel. In these materials, reaction rates and fuel levels, instead of equilibrium composition, determine properties such as lifetime, stiffness, and self-regeneration capability. Fibers exhibit strongly nonlinear behavior including stochastic collapse and simultaneous growth and shrinkage, reminiscent of microtubule dynamics.