In this work, we study LLMs from a carbon emission perspective, addressing both operational and embodied emissions, and paving the way for sustainable LLM serving. We characterize the performance and energy of LLaMA with 1B, 3B, and 7B parameters using two Nvidia GPU types, a latest-generation RTX6000 Ada and an older-generation T4. We analytically model operational carbon emissions based on energy consumption and carbon intensities from three grid regions -- each representing a different energy source mix, and embodied carbon emissions based on chip area and memory size. Our characterization and modeling provide us with an in-depth understanding of the performance, energy, and carbon emissions of LLM serving. Our findings highlight the potential for optimizing sustainable LLM serving systems by considering both operational and embodied carbon emissions simultaneously.