Echo chambers, i.e. clusters of users exposed to news and opinions in line with their previous beliefs, were observed in many online debates on social platforms. We propose a completely unbiased entropy-based method for detecting echo chambers. The method is completely agnostic to the nature of the data. In the Italian Twitter debate about the Covid-19 vaccination, we find a limited presence of users in echo chambers (about 0.35% of all users). Nevertheless, their impact on the formation of a common discourse is strong, as users in echo chambers are responsible for nearly a third of the retweets in the original dataset. Moreover, in the case study observed, echo chambers appear to be a receptacle for disinformative content.