Climate communication is often seen by the NLP community as an opportunity for machine translation, applied to ever smaller languages. However, over 90% the world’s linguistic diversity comes from languages with ‘primary orality’ and mostly spoken in non-Western oral societies. A case in point is the Aboriginal communities of Northern Australia, where we have been conducting workshops on climate communication, revealing shortcomings in existing communication practices along with new opportunities for improving intercultural communication. We present a case study of climate communication in an oral society, including the voices of many local people, and draw several lessons for the research program of NLP in the climate space.