Forecasting the Consumer Price Index (CPI) is an important yet challenging task in economics, where most existing approaches rely on low-frequency, survey-based data. With the recent advances of large language models (LLMs), there is growing potential to leverage high-frequency online text data for improved CPI prediction, an area still largely unexplored. This paper proposes LLM-CPI, an LLM-based approach for CPI prediction inference incorporating online text time series. We collect a large set of high-frequency online texts from a popularly used Chinese social network site and employ LLMs such as ChatGPT and the trained BERT models to construct continuous inflation labels for posts that are related to inflation. Online text embeddings are extracted via LDA and BERT. We develop a joint time series framework that combines monthly CPI data with LLM-generated daily CPI surrogates. The monthly model employs an ARX structure combining observed CPI data with text embeddings and macroeconomic variables, while the daily model uses a VARX structure built on LLM-generated CPI surrogates and text embeddings. We establish the asymptotic properties of the method and provide two forms of constructed prediction intervals. The finite-sample performance and practical advantages of LLM-CPI are demonstrated through both simulation and real data examples.