With a vast amount of data available on online social networks, how to enable efficient analytics over such data has been an increasingly important research problem. Given the sheer size of such social networks, many existing studies resort to sampling techniques that draw random nodes from an online social network through its restrictive web/API interface. While these studies differ widely in analytics tasks supported and algorithmic design, almost all of them use the exact same underlying technique of random walk - a Markov Chain Monte Carlo based method which iteratively transits from one node to its random neighbor. Random walk fits naturally with this problem because, for most online social networks, the only query we can issue through the interface is to retrieve the neighbors of a given node (i.e., no access to the full graph topology). A problem with random walks, however, is the "burn-in" period which requires a large number of transitions/queries before the sampling distribution converges to a stationary value that enables the drawing of samples in a statistically valid manner. In this paper, we consider a novel problem of speeding up the fundamental design of random walks (i.e., reducing the number of queries it requires) without changing the stationary distribution it achieves - thereby enabling a more efficient "drop-in" replacement for existing sampling-based analytics techniques over online social networks. Technically, our main idea is to leverage the history of random walks to construct a higher-ordered Markov chain. We develop two algorithms, Circulated Neighbors and Groupby Neighbors Random Walk (CNRW and GNRW) and rigidly prove that, no matter what the social network topology is, CNRW and GNRW offer better efficiency than baseline random walks while achieving the same stationary distribution. We demonstrate through extensive experiments on real-world social networks and synthetic graphs the superiority of our techniques over the existing ones.