Most individuals in social networks experience a so-called Friendship Paradox: they are less popular than their friends on average. This effect may explain recent findings that widespread social network media use leads to reduced happiness. However the relation between popularity and happiness is poorly understood. A Friendship paradox does not necessarily imply a Happiness paradox where most individuals are less happy than their friends. Here we report the first direct observation of a significant Happiness Paradox in a large-scale online social network of $39,110$ Twitter users. Our results reveal that popular individuals are indeed happier and that a majority of individuals experience a significant Happiness paradox. The magnitude of the latter effect is shaped by complex interactions between individual popularity, happiness, and the fact that users cluster assortatively by level of happiness. Our results indicate that the topology of online social networks and the distribution of happiness in some populations can cause widespread psycho-social effects that affect the well-being of billions of individuals.