The global AI inference market—reaching approximately $90–100 billion annually and growing at 18% CAGR—operates without organized exchange infrastructure. We document three market failures: resource misallocation (80% of China’s newly built compute capacity sits idle), price opacity (100-fold price dispersion across providers of equivalent quality), and unhedged risk exposure (85% of enterprises miss AI cost forecasts by more than 10%). Following the market design tradition of Roth [2002] and Budish et al. [2015], we propose the AI Service Right (ASR) as a transferable property right on AI compute and the AI Service Unit (ASU) as a quality-adjusted, cross-platform unit of account grounded in hedonic price theory [Rosen, 1974]. The ASU is modality-neutral: billing prices across text, image, video, and speech modalities are unified via eq-token conversion factors (κimg ≈ 2,667 eq-tokens per image; κvid ≈ 2,667 per second of video; κspc ≈ 7 per second of audio), and modality-appropriate benchmark sets (MMLU/HumanEval for language; FID/CLIP Score for image; FVD/CLIPSIM for video; MMBench for multimodal) supply the quality in dex via PCA. We design a hybrid secondary market architecture synthesizing mechanisms from four orthogonal market traditions: foreign exchange markets (cross-platform exchange rates and PPP-analog arbitrage via the ASU); equity markets (Central Limit Order Book, market making, clearing); electricity markets (Compute Locational Marginal Pricing for spatial scarcity signals); and decentralized finance (Automated Market Maker for long-tail liquidity). We establish nine formal propositions: bilateral trading is generically inefficient; Compute Locational Marginal Pricing decomposes nodal prices into system marginal cost, capacity congestion, and bandwidth premia; no-arbitrage equi librium holds with capital constraints (extending Shleifer and Vishny 1997); the ASR market Pareto-improves over bilateral trading; market prices are more in formative under ASR; the hybrid CLOB-AMM architecture weakly dominates either mechanism alone; platform adoption admits multiple equilibria with a coordination trap; financialization may improve or reduce price informativeness depending on speculator-hedger composition; and a hedonic micro-foundation justifies the ASU definition. Calibrated agent-based simulation (500 steps, 30 Monte Carlo runs) provides computational validation: the hybrid architecture reduces price dispersion by 90% relative to bilateral trading, and order-of-magnitude welfare estimates suggest enterprise procurement cost savings of 0.2–20% (net of ASR transaction costs; see Table 7) and potential TFP gains from compute reallocation of up to $29.9 billion annually. We propose a phased implementation roadmap from shadow ledger to full financialization, and we engage critically with the concern that financialization may not reduce intermediation costs [Philippon, 2015].