contrast (ca. $20\%$) close to the one measured on the reflectivity maps (ca. $15\%$). This unambigously demonstrates the selective coupling of excitons in one valley to surface plasmons propagating in one direction, thus realizing valley-contrasting chiralitonic states with spins locked to their propagation wavevectors: $$\begin{aligned}
  &&|P^\pm_{K,\sigma^+,-k_{\textrm{\tiny SP}}}> = |g_K,1_{\sigma^+},-k_{\textrm{\tiny SP}}> \pm |e_K,0_{\sigma^+},-k_{\textrm{\tiny SP}}>   \nonumber\\  
  &&|P^\pm_{K',\sigma^-,+k_{\textrm{\tiny SP}}}> = |g_{K'},1_{\sigma^-},+k_{\textrm{\tiny SP}}> \pm |e_{K'},0_{\sigma^-},+k_{\textrm{\tiny SP}}>,   \nonumber  \end{aligned}$$ where $e_{i}(g_{i})$ corresponds to the presence (absence) of an exciton in the valley $i=(K,K')$ of WS$_2$, and $1_{j}(0_{j})$ to 1 $(0)$ plasmon in the mode of polarization $j=(\sigma^+,\sigma^-)$ and wavevector $\pm k_{\textrm{\tiny SP}}$.

The detailed features of SH signal (crosscuts in Fig. \[fig:3\] (c) and (c)) reveal within the bandwidth of our pumping laser the contributions of both the uncoupled excitons and the upper chiraliton to the SH enhancement. The key observation, discussed in the Supporting Information (Sec. D), is the angular dependence of the main SH contribution. This contribution, shifted from the anticrossing region, is a feature that gives an additional proof of the strongly coupled nature of our system because it is determined by the excitonic Hopfield coefficient of the spin-locked chiralitonic state. In contrast, the residual SH signal related to the uncoupled (or 