I know that horses and chins have very similar digestive tracts, so you would think that what is ok for a horse would be the same for the chins.
High quality hay is the only choice of course. Even horses can't get a large amount of Alfalfa, so maybe he was thinking that the hay given to horses was lower quality. I'm not really sure it has been so long since I was told this.
Someone (who has horses) recently mentioned to me that they give horse hay to their chin and I wanted to know for reference if it was ok.
At the risk of derailing the thread, it depends on what you call a "large amount". Alfalfa probably shouldn't normally be free-fed to horses, since it is so rich in protein and energy. However, many people do feed straight alfalfa to their horses, particularly those which need a higher energy intake. A mature 1,100 lb. horse which is used only for light work will need about 16 lbs. of alfalfa per day, as compared to about 22 lbs. of timothy hay, in order to meet its dietary requirements. Horses can also be kept on an alfalfa pasture, as long as the horse is given time to adjust to the diet over the course of a few weeks.
My own horse eats only alfalfa hay as forage in the winter (largely because it's nearly impossible to find any type of grass hay besides brome in this area, and he refuses to eat brome -- he would prefer to starve). He gets about 20 lbs. of alfalfa per day and he does perfectly fine on it. At age 31, he is fat and healthy, and looks about 10 years younger than he is.
For the record, I have regularly fed horse hay (straight brome, or alfalfa/brome mix) to my rabbits. They've done well on it. As others have mentioned, good horse hay is generally very high-quality, and if it's suitable for a horse, it should be just fine for a rabbit or chinchilla (grass hay, that is).