Almost all approaches to multiobjective optimization are based on Genetic Algorithms (GAs), and implementations based on Evolution Strategies (ESs) are very rare. Thus, it is crucial to investigate how ESs can be extended to multiobjective optimization, since they have, in the past, proven to be powerful single objective optimizers. In this paper, we present a new approach to multiobjective optimization, based on ESs. We call this approach the Multiobjective Elitist Evolution Strategy (MEES) as it incorporates several mechanisms, like elitism, that improve its performance. When compared with other algorithms, MEES shows very promising results in terms of performance.