Three-dimensional (3D) topological materials exhibit much richer phenomena than their lower-dimensional counterparts. Here, we propose self-localized topological states (i.e., topological solitons) in a 3D nonlinear photonic Chern insulator. Despite being in the bulk and self-localized in all 3D, the topological solitons at high-symmetry points $K$ and $K^{\prime }$ rotate in the same direction, due to the underlying topology. Specifically, under the saturable nonlinearity the solitons are stable over a broad frequency range. Our results highlight how topology and nonlinearity interact with each other and can be extended to other 3D topological systems.

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• Optical solitons
• Topological effects in photonic systems
• Topological materials