Large language models (LLMs) offer new opportunities for adaptive educational support; however, general-purpose conversational agents may lack the contextual and pedagogical grounding required for laboratory learning, where appropriate assistance depends on the learner's ongoing experimental activity. This paper presents ChemWISE (Chemistry Workflow and Intelligent Scaffolding Environment), a context- and evidence-aware LLM-supported intelligent tutoring system designed for chemistry laboratory learning. ChemWISE integrates LLM interaction with the laboratory workflow by dynamically assembling experiment context, learner knowledge level, procedural state, verified experimental observations, recent tutoring history, and the learner's current message. An evidence hierarchy distinguishes verified system state from student-reported information, canonical experiment instructions, and general chemistry knowledge, while preserving unavailable experimental information as unknown. The tutoring architecture combines this contextual grounding with Socratic questioning, Claim–Evidence–Reasoning (CER), progressive scaffolding, proactive tutoring, and laboratory-safety constraints. The system was developed through an iterative, educator-led, prompt-driven process, in which pedagogical requirements were translated into operational specifications, implemented with AI assistance, and refined through inspection and functional testing. The resulting artifact satisfied the predefined technical requirements and received favorable technical (M = 4.69, SD = 0.57) and pedagogical (M = 4.53, SD = 0.50) expert evaluations. The resulting architecture demonstrates an approach for translating chemistry-laboratory pedagogy into executable, context-grounded LLM tutoring behavior and establishes a validated artifact for subsequent learner-outcome evaluation.