Conventionally, nonreciprocity in time-varying systems is achieved by exploiting both temporal and spatial modulations. In this paper, we introduce a concept of magnetless bianisotropic time-modulated systems that support nonreciprocal wave propagation at the fundamental frequency and use only uniform, solely temporal material modulations. We theoretically explain the nonreciprocal effect by analyzing wave propagation in an unbounded, spatially uniform bianisotropic time-modulated medium. As a simple practical implementation, we design a deeply sub-wavelength bianisotropic metasurface which incorporates a single time-modulated capacitive layer backed by a usual dielectric layer.