In this paper, we propose that paper circuitry provides a productive space for exploring aspects of computational thinking, an increasingly critical 21st century skills for all students. We argue that the creation and operation of paper circuits involve learning about computational concepts such as rule-based constraints, operations, and defined states. Moreover, paper circuitry materials are low cost, provide a low threshold to entry, and draw upon the familiarity that already exists with respect to paper as a hands-on and interactive medium. Paper circuitry thus provides multiple points of entry for students who are unfamiliar with computational thinking ideas while also supporting creative, artistic and crafting activities. It also provides an important alternative to the typically steep learning curve associated with learning a programming language. We define paper circuitry and associated technologies, show how they afford key dimensions of computational thinking, and present examples of paper circuit projects created by students.