Establishing a national comprehensive PNT (Positioning, Navigation, and Timing) system has become a consensus among major countries worldwide. As a crucial component in completing the entire PNT system, the 5G NR (new radio) time service signal plays a vital role. This paper proposes a 5G NR time service signal that uses a spread spectrum system, shares the 5G signal frequency band, but does not occupy the bandwidth of the 5G communication signal. This timing service signal has relatively low power, making it appear “submerged” within the power of the 5G communication signal. The spread spectrum code for this timing signal employs the chaotic orthogonal composite sequence proposed in this paper. Compared to traditional spread spectrum sequences, this sequence offers better security than m-sequences, improved autocorrelation than Walsh sequences, and an effective suppression of the short-period characteristics exhibited when the Skew Tent-Map chaotic sequence takes special values. This paper simulates the capture of the 5G NR time service signal in an environment with a signal-to-noise ratio of 10 dB using an FFT-based parallel code phase search algorithm, successfully capturing the 5G NR time service signal and verifying the feasibility of the proposed chaotic orthogonal composite sequence as a spread spectrum code.