The success of Bitcoin largely relies on the perception of a fair underlying peer-to-peer protocol: blockchain. Fairness here essentially means that the reward (in bitcoins) given to any participant that helps maintain the consistency of the protocol by mining, is proportional to the computational power devoted by that participant to the mining task. Without such perception of fairness, honest miners might be disincentivized to maintain the protocol, leaving the space for dishonest miners to reach a majority and jeopardize the consistency of the entire system. We prove, in this paper, that blockchain is actually unfair, even in a distributed system of only two honest miners. In a realistic setting where message delivery is not instantaneous, the ratio between the (expected) number of blocks committed by two miners is at least exponential in the product of the message delay and the difference between the two miners' hashrates. To obtain our result, we model the growth of blockchain, which may be of independent interest. We also apply our result to explain recent empirical observations and vulnerabilities.