Stencil computations are commonly used in a wide variety of scientific applications, ranging from largescale weather prediction to solving partial differential equations. Stencil computations are characterized by three properties: (1) low arithmetic intensity, (2) limited temporal data reuse, and (3) regular and predictable data access pattern. As a result, stencil computations are typically bandwidth-bound workloads, which only experience limited benefits from the deep cache hierarchy of modern CPUs. In this work, we propose Casper, a near-cache accelerator consisting of specialized stencil computation units connected to the last-level cache (LLC) of a traditional CPU. Casper is based on two key ideas: (1) avoiding the cost of moving rarely reused data throughout the cache hierarchy, and (2) exploiting the regularity of the data accesses and the inherent parallelism of stencil computations to increase overall performance. With minimal changes in LLC address decoding logic and data placement, Casper performs stencil computations at the peak LLC bandwidth. We show that by tightly coupling lightweight stencil computation units near LLC, Casper improves performance of stencil kernels by 1.65× on average (up to 4.16×) compared to a commercial high-performance multi-core processor, while reducing system energy consumption by 35% on average (up to 65%). Casper provides 37× (up to 190×) improvement in performance-per-area compared to a state-of-the-art GPU.