This paper focuses on the privacy risks of disclosing the community structure in an online social network. By exploiting the community affiliations of user accounts, an attacker may infer sensitive user attributes. This raises the problem of community structure deception (CSD), which asks for ways to minimally modify the network so that a given community structure maximally hides itself from community detection algorithms. We investigate CSD through an information-theoretic lens. To this end, we propose a community-based structural entropy to express the amount of information revealed by a community structure. This notion allows us to devise residual entropy minimization (REM) as an efficient procedure to solve CSD. Experimental results over 9 real-world networks and 6 community detection algorithms show that REM is very effective in obfuscating the community structure as compared to other benchmark methods.