Expressive speech-to-speech translation (S2ST) is a key research topic in seamless communication, which focuses on the preservation of semantics and speaker vocal style in translated speech. Early works synthesized speaker style aligned speech in order to directly learn the mapping from speech to target speech spectrogram. Without reliance on style aligned data, recent studies leverage the advances of language modeling (LM) and build cascaded LMs on semantic and acoustic tokens. This work proposes SeamlessExpressiveLM, a single speech language model for expressive S2ST. We decompose the complex source-to-target speech mapping into intermediate generation steps with chain-of-thought prompting. The model is first guided to translate target semantic content and then transfer the speaker style to multi-stream acoustic units. Evaluated on Spanish-to-English and Hungarian-to-English translations, SeamlessExpressiveLM outperforms cascaded LMs in both semantic quality and style transfer, meanwhile achieving better parameter efficiency.