We report a new site for the \textsl{s}-process in rotating massive metal-poor stars. Above a critical rotation speed, such stars evolve in a quasi-chemically-homogeneous fashion, which gives rise to a prolific \textsl{s}-process. Rotation-induced mixing results in primary production of $^{13}$C, which subsequently makes neutrons via $^{13}\mathrm{C}(\alpha,\mathrm{n})^{16}\mathrm{O}$ during core He burning. Neutron capture can last up to $\sim 10^{13}\,\mathrm{s}$ with the peak central neutron density ranging from $\sim10^7$ to $10^{8}\,\mathrm{cm}^{-3}$. Depending on the rotation speed and the mass loss rate, a strong \textsl{s}-process can occur with production of elements up to Bi for progenitors with initial metallicities of $[Z]\lesssim -1.5$. This result suggests that rapidly-rotating massive metal-poor stars are likely the first site for the main \textsl{s}-process. We find that these stars can potentially explain the early onset of the \textsl{s}-process and some of the carbon-enhanced metal-poor (CEMP-\textsl{s} and CEMP-\textsl{r/s}) stars with strong enrichment attributed to the \textsl{s}-process or a mixture of the \textsl{r}-process and the \textsl{s}-process.