In this paper, we present a class of explicit numerical methods for stiff Itô stochastic
differential equations (SDEs). These methods are as simple to program and to use as the well-known
Euler-Maruyama method, but much more efficient for stiff SDEs. For such problems, it is well
known that standard explicit methods face step-size reduction. While semi-implicit methods can
avoid these problems at the cost of solving (possibly large) nonlinear systems, we show that the step-
size reduction phenomena can be reduced significantly for explicit methods by using stabilization
techniques. Stabilized explicit numerical methods called S-ROCK (for stochastic orthogonal Runge-
Kutta Chebyshev) have been introduced as an alternative
to (semi-) implicit methods for the solution of stiff stochastic systems. In this paper we discuss a
genuine Itô version of the S-ROCK methods which avoid the use of transformation formulas from
Stratonovich to Itô calculus. This is important for many applications. We present two families
of methods for one-dimensional and multi-dimensional Wiener processes. We show that for stiff
problems, significant improvement over classical explicit methods can be obtained. Convergence and
stability properties of the methods are discussed and numerical examples as well as applications to
the simulation of stiff chemical Langevin equations are presented.