This paper introduces a vision of confidential prompting: securing user prompts from untrusted, cloud-hosted large language model (LLM) provider while preserving model confidentiality, output invariance, and compute efficiency. As a first step toward this vision, we present Obfuscated Secure Partitioned Decoding (OSPD), a system built on two key innovations. First, Secure Partitioned Decoding (SPD) isolates user prompts within per-user processes residing in a confidential virtual machine (CVM) on the cloud, which are inaccessible for the cloud LLM while allowing it to generate tokens efficiently. Second, Prompt Obfuscation (PO) introduces a novel cryptographic technique that enhances SPD resilience against advanced prompt reconstruction attacks. Together, these innovations ensure OSPD protects both prompt and model confidentiality while maintaining service functionality. OSPD enables practical, privacy-preserving cloud-hosted LLM inference for sensitive applications, such as processing personal data, clinical records, and financial documents.