I argue that the Bitcoins market is an example of a complex system without a stable equilibrium. The users of Bitcoins fall into two broad categories: 1) Capital gain seekers: who have no functional use for the currency apart from an expectation of capital gains. 2) Functional users: who use the currency to save on transaction costs as it provides a less costly medium of exchange over traditional fiat currencies. I assume that each category consists of mean-variance optimizers, and specify simple evolutionary dynamics for each category. I identify two simple routes to Chaos in the Bitcoins market. If only capital gain seekers are present, then one route to chaos is via the logistic map. If both categories of users matter then a possible route to Chaos is via the delay logistic-Henon map. As Chaos is common in nonlinear maps, and capital gain seekers make the dynamical map nonlinear, the emergence of Chaos in the Bitcoins market is a likely scenario in the presence of capital gain seekers. A policy recommendation follows: in order to pre-empt Chaos in the Bitcoins market, currency exchanges should be allowed to convert Bitcoins into dollars and vice versa if and only if there is an associated transaction involving buying and selling of goods or services or if the Bitcoins are freshly mined. Such a regulation pre-empts Chaos by reducing the impact of capital gain seekers on the virtual currency’s value.