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Solitons are shape preserving waveforms that are ubiquitous across nonlinear dynamical systems from BEC to hydrodynamics, and fall into two separate classes: bright solitons existing in anomalous group velocity dispersion, and switching waves forming 'dark solitons' in normal dispersion. Bright solitons in particular have been relevant to chip-scale microresonator frequency combs, used in applications across communications, metrology, and spectroscopy. Both have been studied, yet the existence of a structure between this dichotomy has only been theoretically predicted. We report the observation of dissipative structures embodying a hybrid between switching waves and dissipative solitons, existing in the regime of vanishing group velocity dispersion where third-order dispersion is dominant, hence termed as 'zero-dispersion solitons'. They are observed to arise from the interlocking of two modulated switching waves, forming a stable solitary structure consisting of a quantized number of peaks. The switching waves form directly via synchronous pulse-driving of a Si3N4 microresonator. The resulting comb spectrum spans 136 THz or 97% of an octave, further enhanced by higher-order dispersive wave formation. This dissipative structure expands the domain of Kerr cavity physics to the regime near to zero-dispersion and could present a superior alternative to conventional solitons for broadband comb generation.