Recently, there has been a growing interest in using online technologies to design protocols for secure electronic voting. The main challenges include vote privacy and anonymity, ballot irrevocability and transparency throughout the vote counting process. The introduction of the blockchain as a basis for cryptocurrency protocols, provides for the exploitation of the immutability and transparency properties of these distributed ledgers. In this paper, we discuss possible uses of the blockchain technology to implement a secure and fair voting system. In particular, we introduce a secret share-based voting system on the blockchain, the so-called SHARVOT protocol. Our solution uses Shamir's Secret Sharing to enable on-chain, i.e. within the transactions script, votes submission and winning candidate determination. The protocol is also using a shuffling technique, Circle Shuffle, to de-link voters from their submissions.