This paper presents Acquisition Thompson Sampling (ATS), a novel algorithm for batch Bayesian Optimization (BO) based on the idea of sampling multiple acquisition functions from a stochastic process. We define this process through the dependency of the acquisition functions on a set of model parameters. ATS is conceptually simple, straightforward to implement and, unlike other batch BO methods, it can be employed to parallelize any sequential acquisition function. In order to improve performance for multi-modal tasks, we show that ATS can be combined with existing techniques in order to realize different explore-exploit trade-offs and take into account pending function evaluations. We present experiments on a variety of benchmark functions and on the hyper-parameter optimization of a popular gradient boosting tree algorithm. These demonstrate the competitiveness of our algorithm with two state-of-the-art batch BO methods, and its advantages to classical parallel Thompson Sampling for BO.