As part of building the smart grid, there is a massive deployment of so-called smart meters that aggregate information and communicate with the back-end office, apart from measuring properties of the local network. Detailed measurements and communication of, e.g., consumption allows for remote billing, but also in finding problems in the distribution of power and overall to provide data to be used to plan future upgrades of the network. From a security perspective, a massive deployment of such Internet of Things (IoT) components increases the risk that some may be compromised or that collected data are used for privacy-sensitive inference of the consumption of households. In this paper, we investigate the privacy concerns regarding detailed readings of smart meters for billing purposes. We present Gridchain, a solution where households can opt-in to hide their consumption patterns and thus make Non-Intrusive Load Monitoring (NILM) more challenging. Households form groups where they can trade real consumption among themselves to achieve reported consumption that would be resistant to NILM. Gridchain is built on a publish/subscribe model and uses a permissioned blockchain to record any trades, meaning that dishonest households can be discovered and punished if they steal from other households in the group or the electricity company in the end. We implement and release a proof-of-concept of Gridchain and use public datasets to allow reproducibility. Our results show that even if an attacker has access to the reported electricity consumption of any member of a Gridchain group, this reported consumption is significantly far from the actual consumption to allow for a detailed fingerprint of the household activities.