Chroma is the conductor of the color orchestra. Unlike many of the other powerful figures in the book, he doesn't give Milo a tangible present. Instead, he gives Milo responsibility, asking him to wake him up in time for the sunrise.
But this responsibility is definitely a gift, just of a different kind. Like the other gifts Milo receives, this responsibility helps him learn some valuable lessons on his own. Spurred on by the small task he's given, Milo decides to reach for the stars. He goes on a conducting spree, thinking he just wants to dabble, and ends up making a mess of everything for a week. But when Chroma wakes up, he actually praises the boy and says that maybe someday Milo can conduct after all. Hmmm.
As you can see, Chroma doesn't discipline Milo or teach him things outright. Instead, Milo uses this experience with Chroma to learn about self-discipline and about taking responsibility for his own actions. Milo learns that he has to figure out when he's ready or not ready to do things, and that he can't depend on other people to do this for him. Who knew a color orchestra could teach you all that?
(Also, don't forget about this guy's name: chroma is the Greek word for color. Once again, Juster names it like it is.)