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In this paper, we explore the prospect of accelerating tree-based genetic programming (TGP) by way of modern field-programmable gate array (FPGA) devices, which is motivated by the fact that FPGAs can sometimes leverage larger amounts of data/function parallelism, as well as better energy efficiency, when compared to general-purpose CPU/GPU systems. In our preliminary study, we introduce a fixed-depth, tree-based architecture capable of evaluating type-consistent primitives that can be fully unrolled and pipelined. The current primitive constraints preclude arbitrary control structures, but they allow for entire programs to be evaluated every clock cycle. Using a variety of floating-point primitives and random programs, we compare to the recent TensorGP tool executing on a modern 8 nm GPU, and we show that our accelerator implemented on a 14 nm FPGA achieves an average speedup of 43×. When compared to the popular baseline tool DEAP executing across all cores of a 2-socket, 28-core (56-thread), 14 nm CPU server, our accelerator achieves an average speedup of 4,902×. Finally, when compared to the recent state-of-the-art tool Operon executing on the same 2-processor CPU system, our accelerator executes about 2.4× slower on average. Despite not achieving an average speedup over every tool tested, our single-FPGA accelerator is the fastest in several instances, and we describe five future extensions that could allow for a 32–144× speedup over our current design as well as allow for larger program depths/sizes. Overall, we estimate that a future version of our accelerator will constitute a state-of-the-art GP system for many applications.