Disordered hyperuniform structures are an exotic state of matter having vanishing long wave-length density fluctuations similar to perfect crystals but without long-range order. Although its importance in materials science has been brought to the fore in the past decade, the rational design of experimentally realizable disordered strong hyperuniform micro-structures remains challenging. Here, by using computer simulations and theoretical analyses, we discover a new type of dynamic disordered fluid state with strong hyperuniformity in 2D systems of chiral active particles where particles perform independent circular motions of the radius R with the same handedness. In the strong driving or zero-noise limit, this system undergoes an absorbing-active transition to form a non-equilibrium strongly hyperuniform fluid. This new hyperuniform fluid features a special length scale, i.e., the diameter of the circular trajectory of particles, below which large density fluctuations as a result of dynamic cluster formation are observed. By developing a dynamic mean-field theory, we show that the dynamic cluster formation can be explained as an motility-induced microphase separation at mean-field level, while the Fickian diffusion at large length scales and local center of mass conserved interaction are responsible for the global hyperuniformity. Our results suggest the possibility of designing active matter system to form hierarchical disordered hyperuniform materials.