Second-order orthogonal Runge-Kutta-Chebyshev methods for stiff deterministic ordinary differential equations are generalized and modified to apply to systems of stiff stochastic differential equations (SSDE) of the form \[ dX(t)= f(X(t))\,dt+ \sum^m_{r=1} g^r(X(t))\,dW_r(t),\quad X(0)= X_0, \] where the \(W_r(t)\) are independent one-dimensional Wiener processes. An explicit method, denoted S-ROCK2, is derived and shown to have weak second-order convergence. Its numerical asymptotic stability domain and its numerical mean-square stability domain are found, and its stability properties are shown to compare favorably to those of other methods for SSDE. Results of numerical experiments are presented that demonstrate the advantages of S-ROCK2.