Readability is referred to as the degree of difficulty to which an given text (article) can be understood by readers. When readers are reading a text with high readability, they will achieve better comprehension and learning retention. However, it has been a long-standing critical challenge to develop effective readability prediction models that can automatically and accurately assess the readability of a given text. When building readability prediction models for the Chinese language, word segmentation ambiguity is often a knotty problem that will inevitably happen in the pre-processing of texts. In view of this, we present in this paper a novel readability prediction approach for the Chinese language, building on a recently proposed, so-called Bidirectional Encoder Representation from Transformers (BERT) model that can capture both syntactic and semantic information of a text directly from its character-level representation. With the BERT-based readability prediction model that takes consecutive character-level representations as its input, we effectively assess the readability of a given text without the need of performing error-prone word segmentation. We empirically evaluate the performance of our BERT-based readability prediction model on a benchmark task, by comparing it with a strong baseline that utilizes a celebrated classification model (named fastText) in conjunction with word-level presentations. The results demonstrate that the BERT-based model with character-level representations can perform on par with the fastText-based model with word-level representations, yielding the accuracy of 78.45% on average. This finding also offers the promise of conducting readability assessment of a text in Chinese directly based on character-level representations.