How fast a surface oxide layer is formed on bulk chromium?
First, a definition of the Langmuir unit, used in the graph in the question, which is not often run across except by vacuum (particularly UHV) folks. One Langmuir is the exposure of a surface to a gas pressure of $10^{-6}$ Torr for one second. It roughly corresponds to one monolayer equivalent of gas hitting the surface. At normal atmospheric pressure, with 20% oxygen in air, 1 Langmuir of oxygen hits the surface in about 6.6 nanoseconds (yes, nanoseconds).

Another paper that could be of interest is C. Palacio et al., "AES, XPS and EELS study of the initial oxidation of polycrystalline chromium", Surface Science 182(1-2) 41-55 (1987). They see chemisorption of oxygen in the first 1-2 L, nucleation and lateral growth of oxide islands up to 10 L, and continued growth of an oxide film above 10 L.

Overall, there is not a huge difference between the two papers. By ~10 L of exposure to oxygen there is a continuous oxide on the surface at 300K. Following from the numbers in the first paragraph, that occurs in less than 100 nanoseconds. Basically, it oxidizes as it is cut.