I've been to Chantilly twice, both times day trips from Paris in May.
I'm a thoroughbred racing fan and went to the Chantilly race course twice. If you're interested, you'll want to go to the france-galop website to find out when Chantilly is having its days of races. French racing has three major race courses, Paris Longchamp, Chantilly, and Saint-Cloud, and racing days alternate among those top venues, as well as with smaller courses.
The race course is within easy walking distance from the chateau (a matter of a few hundred yards, really), whose art works are worth viewing. You'll certainly want to walk the expansive grounds as well.
The racing stables with the adjoining horse museum is next to the chateau. The museum was musty and rather unkempt when I went but I think it may have undergone a much-needed renovation since I was there. The exhibits were literally all-things-horses, not just pertaining to thoroughbred race horses, but work horses and show horses as well. This included paintings and other art works, horses carved in wood, a short film, and even horse board games. The horse museum sponsors equestrian events, and I saw some dressage training. The very odd thing about my visit to the stables (which, in addition to the stabled horses, features dozens of carriages from the past) and the museum itself is that I was the only one to tour them during that two-hour period. I was utterly, eerily alone. It was a singular experience.
The horse museum had a small gift shop that was closed when I first got there, but was opened by the young staff when they saw me.