The European chemical industry plays a crucial role in the economy, manufacturing thousands of products that find applications across many sectors. On the other hand, the sector is also one of the largest energy consumers, and emits significant amounts of greenhouse gases, together with toxic, bioaccumulative and persistent chemicals. Acknowledging the need for a shift towards a greener industry model, this contribution assesses the absolute sustainability level of the chemical sector by contrasting the impacts it causes with the ecological capacity of the planet, as given by the planetary boundaries framework. Results indicate that impacts incurred by the European chemical industry transgress CO2-based thresholds significantly, with burdens on atmospheric CO2 concentration, energy imbalance, and ocean acidification being 15, 16 and 6 times larger than planetary limits. The biosphere integrity boundary, assessed here based on functional diversity, is also transgressed by 3 %. The five chemicals with the highest production volume, namely ammonia, polypropylene, high-density polyethylene, styrene, and benzene, are responsible for around 50 % of impacts in all the planetary boundaries. This suggests that they should be the target of dedicated research and policies. Finally, the study assesses a set of improvement pathways for the European chemical industry to become sustainable. It is found that the deployment of carbon capture and storage technologies to compensate for the greenhouse gases emitted by the sector would allow the chemical industry to meet all the planetary boundaries concurrently, yet burden-shifting would still cause other planetary boundaries to be deteriorated. This evidences the need to employ holistic approaches to assess the wide implications of any solution adopted within or outside the chemical industry.