We report Phoenics, a probabilistic global optimization algorithm identifying the set of conditions of an experimental or computational procedure which satisfies desired targets. Phoenics combines ideas from Bayesian optimization with concepts from Bayesian kernel density estimation. As such, Phoenics allows to tackle typical optimization problems in chemistry for which objective evaluations are limited, due to either budgeted resources or time-consuming evaluations of the conditions, including experimentation or enduring computations. Phoenics proposes new conditions based on all previous observations, avoiding, thus, redundant evaluations to locate the optimal conditions. It enables an efficient parallel search based on intuitive sampling strategies implicitly biasing toward exploration or exploitation of the search space. Our benchmarks indicate that Phoenics is less sensitive to the response surface than already established optimization algorithms. We showcase the applicability of Phoenics on the Oregonator, a complex case-study describing a nonlinear chemical reaction network. Despite the large search space, Phoenics quickly identifies the conditions which yield the desired target dynamic behavior. Overall, we recommend Phoenics for rapid optimization of unknown expensive-to-evaluate objective functions, such as experimentation or long-lasting computations.