This study proposes augmenting dialog data with think-aloud utterances (TAUs) for modeling individual personalities in text chat by LLM. TAU is a verbalization of a speaker's thought before articulating the utterance. We expect "persona LLMs" trained with TAU-augmented data can mimic the speaker's personality trait better. We tested whether the trained persona LLMs obtain the human personality with respect to Big Five, a framework characterizing human personality traits from five aspects. The results showed that LLMs trained with TAU-augmented data more closely align to the speakers' Agreeableness and Neuroticism of Big Five than those trained with original dialog data. We also found that the quality of TAU-augmentation impacts persona LLM's performance.