The widespread adoption of LLMs has driven an exponential rise in their deployment, imposing substantial demands on inference clusters. These clusters must handle numerous concurrent queries for different LLM downstream tasks. To handle multi-task settings with vast LLM parameter counts, methods like Low-Rank Adaptation (LoRA) enable task-specific fine-tuning while sharing most of the base LLM model across tasks. Hence, they allow concurrent task serving with minimal memory requirements. However, existing LLM serving systems face inefficiencies: they overlook workload heterogeneity, impose high link bandwidth from frequent adapter loading, and suffer from head-of-line blocking in their schedulers. To address these challenges, we present Chameleon, a novel LLM serving system optimized for many adapter environments, that relies on two core ideas: adapter caching and adapter-aware scheduling. First, Chameleon caches popular adapters in GPU memory, minimizing the adapter loading times. Importantly, it uses the otherwise idle GPU memory, avoiding extra memory costs. Second, Chameleon uses a non-preemptive multi-queue scheduling to efficiently account for workload heterogeneity. In this way, Chameleon simultaneously prevents head of line blocking and starvation. We implement Chameleon on top of a state-of-the-art LLM serving platform and evaluate it with real-world production traces and open-source LLMs. Under high loads, Chameleon reduces P99 and P50 TTFT latency by 80.7% and 48.1%, respectively, while improving throughput by 1.5x compared to state-of-the-art baselines.