The rapid adoption of large language model (LLM)-based systems -- from chatbots to autonomous agents capable of executing code and financial transactions -- has created a new attack surface that existing security frameworks inadequately address. The dominant framing of these threats as "prompt injection" -- a catch-all phrase for security failures in LLM-based systems -- obscures a more complex reality: Attacks on LLM-based systems increasingly involve multi-step sequences that mirror traditional malware campaigns. In this paper, we propose that attacks targeting LLM-based applications constitute a distinct class of malware, which we term \textit{promptware}, and introduce a five-step kill chain model for analyzing these threats. The framework comprises Initial Access (prompt injection), Privilege Escalation (jailbreaking), Persistence (memory and retrieval poisoning), Lateral Movement (cross-system and cross-user propagation), and Actions on Objective (ranging from data exfiltration to unauthorized transactions). By mapping recent attacks to this structure, we demonstrate that LLM-related attacks follow systematic sequences analogous to traditional malware campaigns. The promptware kill chain offers security practitioners a structured methodology for threat modeling and provides a common vocabulary for researchers across AI safety and cybersecurity to address a rapidly evolving threat landscape.