This paper studies public opinion in the context of strong social norms. We present a model that highlights how social pressure can affect the public expression of opinion either through a change in publicly stated views (conformity) or by inducing self-censorship (silence). In several pre-registered online experiments in the US, we elicit participants' views on two controversial issues (gender and race) and their willingness to publish these views online in an incentivized manner. The empirical patterns are consistent with the presence of ideologically left-wing social norms: participants who held left-wing views were more willing to publish these. We then manipulate social pressure in three different ways. First, making participants aware of the prospect for publication results in conformity to the left-wing norm. Second, informing participants that a lower share of previous participants were willing to publish their views results in a lower willingness to publish. Finally, priming participants with the threat of online social backlash reduces their willingness to speak up (though explicit mention of "cancel culture" increases speaking up within a sub-sample).