Spin-wave based transmission and processing of information is a promising emerging nano-technology that can help overcome limitations of traditional electronics based on the transfer of electrical charge. Among the most important challenges for this technology is the implementation of spin-wave devices that can operate without the need for an external bias magnetic field. Here we experimentally demonstrate that this can be achieved using sub-micrometer wide spin-wave waveguides fabricated from ultrathin films of low-loss magnetic insulator - Yttrium Iron Garnet (YIG). We show that these waveguides exhibit a highly stable single-domain static magnetic configuration at zero field and support long-range propagation of spin waves with gigahertz frequencies. The experimental results are supported by micromagnetic simulations, which additionally provide information for optimization of zero-field guiding structures. Our findings create the basis for the development of energy-efficient zero-field spin-wave devices and circuits.