It starts with Celeron Broadwell-U, Pentium Broadwell-U as well as 5th Generation Core i3, i5 and even i7 parts based on Broadwell-U.
This is happening right now, and Intel plans to update all these Chromebooks in Q4 with the new Skylake processors. The top one is based on a Skylake-U Core i5 or Core i7 processor, no surprises there. Intel plans to replace Broadwell-U Core i3 with a Skylake-U Core i3, and obviously the rest of the line gets the same treatment.
The Broadwell-U based Pentium will get a Skylake-based Pentium replacement, and there will be a Celeron based Skylake, all planned for Q4 2015. Intel will debut with Chromebook based on Core M silicon, and as far as we know this will be the first Core M Chromebook. We expect it to be fast and efficient, but we are curious about pricing, as Core M parts don't tend to come cheap.
These are Intel's current plans and they can be changed as always. Intel has Skylake silicon back and it even benchmarked it under Windows 8.1, showing some promising numbers.
Most Chromebooks in the market sit between $200 and $300 USD and are based on either Celerons or Pentiums and rarely on Core i3. So maybe Core i5 and Core i7 based machines will appear sometime in the future.