Package-level integration using multi-chip-modules (MCMs) is a promising approach for building large-scale systems. Compared to a large monolithic die, an MCM combines many smaller chiplets into a larger system, substantially reducing fabrication and design costs. Current MCMs typically only contain a handful of coarse-grained large chiplets due to the high area, performance, and energy overheads associated with inter-chiplet communication. This work investigates and quantifies the costs and benefits of using MCMs with fine-grained chiplets for deep learning inference, an application area with large compute and on-chip storage requirements. To evaluate the approach, we architected, implemented, fabricated, and tested Simba, a 36-chiplet prototype MCM system for deep-learning inference. Each chiplet achieves 4 TOPS peak performance, and the 36-chiplet MCM package achieves up to 128 TOPS and up to 6.1 TOPS/W. The MCM is configurable to support a flexible mapping of DNN layers to the distributed compute and storage units. To mitigate inter-chiplet communication overheads, we introduce three tiling optimizations that improve data locality. These optimizations achieve up to 16% speedup compared to the baseline layer mapping. Our evaluation shows that Simba can process 1988 images/s running ResNet-50 with batch size of one, delivering inference latency of 0.50 ms.