The growing data economy features a complex ecosystem of organizations, individuals, and devices. With digital data exchange between entities becoming ubiquitous in modern society, there is a need for carbon cost estimates that span the entire life cycle of data. We argue that accounting at the granularity of an application, process, or request can be augmented by a scheme that associates carbon annotations with data. Such a scheme would preserve continuity between interacting entities in the data economy to ensure that carbon costs are accounted for across the entire value chain of data. In short, the contributions of this paper are (1) a vision toward tracking the life cycle carbon emissions of data, as well as (2) several techniques for reducing these life cycle costs. In particular, we define the distinction between embodied carbon from data collection, transfer, and storage, and operational carbon from data use.