This paper studies public opinion in the context of strong social norms that can induce conformity and self-censorship. 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 a series of pre-registered online experiments in the US, we elicit participants’ views on two controversial topics (race and gender) 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 their opinions, and those who were randomly made aware of the prospect of publication reported less conservative views. A priming information treatment, in which participants were informed about cancel culture and the potential negative backlash from social media posts, induced some conformity and silencing, but the results were generally weak and not statistically significant. Finally, a social information treatment, which informed respondents about high rates of others’ willingness to speak up, significantly decreased self-censorship. We use our theoretical model, and empirical estimates from the experiment about the value of "speaking up", to analyze potential welfare implications. The analysis reveals that social norms which restrict freedom of expression may enhance social welfare.