Non-formal learning environments, such as science museums, have a fundamental role in science education and high potentialities as ideal contexts for science teachers’ training. These aspects have been analyzed and reported in several recent works mainly focused on students’ perception of science and increased engagement towards scientific disciplines. In this work, a project-based learning methodology optimized and experimented in the frame of a pre-service chemistry teachers’ course at the University of Pisa (Italy), during the last eight years, involving in total 171 participants, is presented. This educational project has several distinctive features related to the STEAM philosophy, with a high level of multi-disciplinarity and creativity. Most of the laboratories and chemistry-centered activities were conceived, planned and carried out by the future chemistry teachers in non-formal contexts, such as science museums. A case study based on a series of non-formal laboratories designed by a group of students during their training in the academic year 2018–2019 and performed in a science museum is reported and examined in details. In this paper, all steps of the STEAM project-based learning methodology are described underlining the main learning outcomes and cognitive levels involved in each step and the relevant methodologies proposed during the training course and adopted in the project. The effectiveness of this pre-service teachers’ training methodology is finally discussed in terms of participants’ motivation and interest towards the course’s content, students’ final judgment of their training experiences and, in particular, of the STEAM project-based learning activities. From the students’ feedbacks and final assessment, the role of the non-formal context in teaching and learning chemistry and the efficacy of developing educational activities related to current and real-life chemistry-centered topics emerged as very positive aspects of the proposed approach.