This paper proposes a Hilbert space embedding for Dirichlet Process mixture models via a stick-breaking construction of Sethuraman. Although Bayesian nonparametrics offers a powerful approach to construct a prior that avoids the need to specify the model size/complexity explicitly, an exact inference is often intractable. On the other hand, frequentist approaches such as kernel machines, which suffer from the model selection/comparison problems, often benefit from efficient learning algorithms. This paper discusses the possibility to combine the best of both worlds by using the Dirichlet Process mixture model as a case study.