Tipping elements are components of the Earth system that could be pushed into qualitatively different states by small external perturbations, with profound environmental impacts possibly endangering the livelihoods of millions of people. There are indications for significant interlinkages between climate tipping elements and even the potential for tipping cascades or domino effects from the climate to the social sphere. We will assess these effects for a highly relevant tipping chain connecting climatic tipping elements like Antarctica and Greenland with potential social tipping processes in public opinion formation and climate policy changes, and their societal implications.