Laboratory coursework is widely considered to be an integral part of chemistry undergraduate degree programs, although its impact on students' chemistry knowledge is largely unsubstantiated. Laboratory experiences provide opportunities to learn skills beyond chemistry content knowledge, such as how to use scientific instrumentation appropriately, how to gather and analyze data, and how to work in a team. The acquisition of process skills, including critical thinking, problem solving, and communication, is an integral part of becoming a scientist and participating in the scientific community. As apprentice scientists, chemistry students interact with each other in a context-rich environment where the need for process skills can arise organically. This study seeks to understand the role of laboratory courses in developing process skills. Students in a first-year chemistry laboratory course used rubrics to assess their own process skills. During the course, the students also received feedback via rubrics from a teaching assistant trained in rubric use. Additionally, students reported their understanding of process skills and their perceived improvements over the course of the semester. Our results suggest that students understand group dynamics process skills such as teamwork and communication better than they understand cognitive process skills such as critical thinking and information processing. While the evidence further suggests that students improved their process skills, and students reported that they improved their process skills, they showed inconsistent abilities to self-assess and provide justification for their assessment using rubrics.