Is there a relationship between the frequency of characters and their respective complexity? This hypothesis, which we may call the Principle of Least Complexity, was recently tested across a number of scripts across the world (Koshevoy et al., 2023). However, this hypothesis has not yet been comprehensively tested on the Chinese language. Because Chinese also varies in complexity both within and between scripts (simplified versus traditional), it is important to determine to what degree the overall relationship varies within and between Chinese scripts. In this article, we first report an initial exploratory analysis on Cantonese frequency data which spawned our investigation of this question. Then we discuss a confirmatory analysis on an additional dataset composed of simplified characters. Finally, we followed up with another exploratory analysis comparing Mandarin and Cantonese frequencies. Across all three analyses, the outcome was clear, as the association between complexity and frequency was negative across contexts. However, the association, while statistically significant, was very weak. Moreover, the differences in associations with respect to scripts and spoken languages were negligible. The findings lend credit to the Principle of Least Complexity as a factor in Chinese, but diminish its standing with respect to its practical significance in reading research.