Samsung's flagships last year, the Galaxy S7 and S7 Edge, were powered by either Qualcomm's Snapdragon 820, or Samsung's Exynos 8 Octa processor, depending on the market.
Ever since the rumors about the Galaxy S8 and S8+ started floating around, we have been hearing about the Snapdragon 835, which the devices will feature. However, it is highly possible that some markets will receive phones powered by an Exynos 9 processor, which is yet to be announced.
According to a tease from the Korean company, they will announce their latest chipset soon, so it is very likely that it will power the Galaxy S8 and S8+, at least in certain markets.
No details have been released for now, but the Exynos 9 should be manufactured using Samsung's own 10nm process, like the Snapdragon 835.
Previous rumors have suggested that the Exynos 9 will have an octa-core CPU with four custom M2 cores and four ARM Cortex-A53 cores, and the new ARM Mali-G71 GPU.