Large language models (LLMs) have demonstrated remarkable performances on a wide range of natural language tasks. Yet, LLMs' successes have been largely restricted to tasks concerning words, sentences, or documents, and it remains questionable how much they understand the minimal units of text, namely characters. In this paper, we examine contemporary LLMs regarding their ability to understand character composition of words, and show that most of them fail to reliably carry out even the simple tasks that can be handled by humans with perfection. We analyze their behaviors with comparison to token level performances, and discuss the potential directions for future research.