The reliability of nuclear command, control and communications has long been identified as a critical component of the strategic stability among nuclear states. Advances in offensive cyber weaponry have the potential to negatively impact this reliability, threatening strategic stability. In this paper we present a game theoretic model of preemptive cyber attacks against nuclear command, control and communications. The model is a modification of the classic two-player game of Chicken, a standard game theoretic model for nuclear brinksmanship. We fully characterize equilibria in both the complete information game and two distinct two-sided incomplete information games. We show that when both players have advanced cyber capabilities conflict is more likely in equilibrium, regardless of information structure. On the other hand, when at most one player has advanced cyber capabilities, strategic stability depends on the information structure. Under complete information, asymmetric cyber capabilities have a stabilizing effect in which the player with strong cyber has the resolve to stand firm in equilibrium. Under incomplete information, asymmetric cyber capabilities can have both stabilizing and destabilizing effects depending on prior beliefs over opponent cyber capabilities.