This essay is about the rules and laws of science, and the way they let us down. I will make the unusual argument that, for science to be ethical, a strong element of lawlessness is needed. But what is an ethical science? Amongst other things, it is one where a scientist’s individual autonomy, intellectual and otherwise, is harmonised with social responsibility. This happy balance is somewhat threatened by the realities of a high-pressure research culture. Professional anxiety, therefore, gives a background hum to my argument. However, my more explicit theme concerns the laws of science, and their grip on the imagination of scientists. I explore, in particular, the idea that the image of a lawlike science lessens the ability of researchers to see what is right and good in their work. As a corrective I consider an alternative, lawless conception of science. To make this vision of science as effective as possible, I conceive a magnificent painted triptych, filled with examples and allegories. It will hang in the foyers and even the laboratories of our science institutes and is called “The Triptych of Lawlessness”.