Elemental abundances of stars are the result of the complex enrichment history of their galaxy. Interpretation of observed abundances requires flexible modeling tools to explore and quantify the information about Galactic chemical evolution (GCE) stored in such data. Here we present Chempy, a newly developed code for GCE modeling, representing a parametrized open one-zone model within a Bayesian framework. A Chempy model is specified by a set of five to ten parameters that describe the effective galaxy evolution along with the stellar and star-formation physics: for example, the star-formation history (SFH), the feedback efficiency, the stellar initial mass function (IMF), and the incidence of supernova of type Ia (SN Ia). Unlike established approaches, Chempy can sample the posterior probability distribution in the full model parameter space and test data-model matches for different nucleosynthetic yield sets. It is essentially a chemical evolution fitting tool. We straightforwardly extend Chempy to a multi-zone scheme. As an illustrative application, we show that interesting parameter constraints result from only the ages and elemental abundances of the Sun, Arcturus, and the present-day interstellar medium (ISM). For the first time, we use such information to infer the IMF parameter via GCE modeling, where we properly marginalize over nuisance parameters and account for different yield sets. We find that 11.6 +2.1 −1.6 % of the IMF explodes as core-collapse supernova (CC-SN), compatible with Salpeter (1955, ApJ, 121, 161). We also constrain the incidence of SN Ia per 10 3 M to 0.5−1.4. At the same time, this Chempy application shows persistent discrepancies between predicted and observed abundances for some elements, irrespective of the chosen yield set. These cannot be remedied by any variations of Chempy's parameters and could be an indication of missing nucleosynthetic channels. Chempy could be a powerful tool to confront predictions from stellar nucleosynthesis with far more complex abundance data sets and to refine the physical processes governing the chemical evolution of stellar systems.