There exist both scalable tasks, like reading comprehension and fact-checking, where model performance improves with model size, and unscalable tasks, like arithmetic reasoning and symbolic reasoning, where model performance does not necessarily improve with model size. Large language models (LLMs) equipped with Chain-of-Thought (CoT) prompting are able to make accurate incremental predictions even on unscalable tasks. Unfortunately, despite their exceptional reasoning abilities, LLMs tend to internalize and reproduce discriminatory societal biases. Whether CoT can provide discriminatory or egalitarian rationalizations for the implicit information in unscalable tasks remains an open question. In this study, we examine the impact of LLMs' step-by-step predictions on gender bias in unscalable tasks. For this purpose, we construct a benchmark for an unscalable task where the LLM is given a list of words comprising feminine, masculine, and gendered occupational words, and is required to count the number of feminine and masculine words. In our CoT prompts, we require the LLM to explicitly indicate whether each word in the word list is a feminine or masculine before making the final predictions. With counting and handling the meaning of words, this benchmark has characteristics of both arithmetic reasoning and symbolic reasoning. Experimental results in English show that without step-by-step prediction, most LLMs make socially biased predictions, despite the task being as simple as counting words. Interestingly, CoT prompting reduces this unconscious social bias in LLMs and encourages fair predictions.