We have proposed a novel design for an asynchronous computing device based on Chemical Reaction Networks. CRNs are inherently asynchronous, and thus particularly well suited to this computational paradigm. Our designs are based on a simple, bi-molecular reaction motif inspired by Approximate Majority (Angluin et al. 2008; Cardelli and Csikász-Nagy 2012), employ catalytic reactions and assume well-mixed solution and constant, uniform rates. Moreover, they do not rely on the universal clock which is difficult to realise. Since an arbitrary CRN can be physically realised using DNA strand displacement (Soloveichik et al. 2010), as recently demonstrated experimentally in Chen et al. (2013), the proposed designs are in principle implementable, and we have confirmed this in theory by modelling them in the two-domain setting (Cardelli 2010) using Visual DSD (Phillips and Cardelli 2009; Lakin et al. 2011). Our designs are the first feasible implementation of an asynchronous computing device in chemical kinetics and are relevant for a multitude of applications in nanotechnology and synthetic biology. As future work we would like to investigate alternative experimental settings.