This paper offers a linguistic approach to narrative analysis, illustrated through a quantitative/qualitative lexico-semantic study of sustainability reports by BP, Equinor, ConocoPhillips, and ExxonMobil. It contributes novel insights into how major CO2 emitters present themselves in climate narratives. My aim is, first, to show how the basic components of narratives (Complication, Reaction, and Resolution) and the classic character set (victim, villain, and hero) may be identified through linguistic features, and second, to consider how the special nature of climate change impacts on the enactment of this character set. The study considers whether the companies acknowledge their reputation as villains in the global climate narrative, or whether they are discursively shying away from this script. I find that the reports share a basic climate narrative, representing a techno-optimistic approach to maintaining a profitable business in a carbon-constrained society, with gas representing a narrative Complication as well as a Resolution. The global villain role is acknowledged, but typically softened through a dual villain/hero role. The hero role in fact turned out to be the most conspicuous in the material.