For what it’s worth, I’ll offer an alternative to Ian’s approach. Whenever I am doing fingerboard repairs, even small chips that will be visible outside of footprint of the fretwire bead, I always prefer to make the repair using wood. I choose a donor wood that is as close a match to the board in color, type and wood grain as I can find in my scrap wood drawer. the bigger your variety of scraps to choose from obviously helps in the end result.
I cut in a sliver that sits proud of the board – glue it in with either cyanoacrylate or hide glue depending on how much of a hurry I am in (most of the time I default to CA). After the glue is dry, i can file or sand it flush with the board and, most of the time, get a trouble free, permanent and invisible repair.
Here are some pictures to illustrate: