(From The Online Chalky Museum)
What is a "Chalky"?
The term Chalky is most often used to describe models that have been basecoated with white paint before their normal run colors are applied. These models look as though they were carved from chalk and so the name. This practice of bascoating models was most prevelant in 1974 at the height of the oil crisis. At that time Breyer was using cheaper plastics that were either partially or entirely non-white and so these needed to be painted white first. Green, Purple, Pink, Grey, and Black plastic have all been reported. In some additional cases Breyer painted over leftover models from previous runs. This has happened all through Breyer's history from the 1950s to today, but traditionally, when referencing chalky models, collectors are talking about the 1970s era models.
Also during the oil crisis, another secondary type of chalky model emerged. This is what is also known as a "chalky plastic" model. In my experience basecoat and plastic chalkies are almost indistinguishable at first glance. The plastic used to mold the models is itself very opaque white and the paint appears to sit on top of it in the same way it does on a basecoated model, unlike the normal Breyer plastic which absorbs the paint over time. This plastic is also very brittle and the paint jobs are much more fragile. The paint will almost rub off in your hands if you apply a little pressure.
How can I tell a chalky model from a standard model?
If you are unsure whether or not your model is chalky, there are several things you can check. Many collectors will agree that one good way to identify a basecoated model is to look at the bottom of the hooves. Basecoat chalkies tend to have a very distinct "pooling" effect on the underside of the hooves. You can imagine a thick coat of paint was applied and then the model was set down on a table while the paint was still wet. Normal models will simply have flat, white plastic on the underside of their hooves. The photo below is of a chalky FAM, and demonstrates this pooling effect.

In some models this pooling effect will also be evident in other areas. The basecoats were often very thick and so detail is lost in the deeper grooves on the mane and tail. You can see in the photo below how the thick paint sits in the lower grooves on this rearing horse's tail.

Another thing you will notice, if your model has any paint rubs, it may be rubbed all the way down to a different color plastic. The rub will have like a bright white halo around a green or grey or black plastic surface. Normal models will simply have rubs down the their normal white plastic. On this jumping horse, for example, you can see by his rubs that he is molded out of grey plastic, painted white, and then painted his bay color.

Chalky plastic models are much harder to describe. They have the same opaque painted white look as basecoated chalky models, but that is the way the plastic is. Many people confuse the two, and I have been sold "genuine basecoat chalky" models that were really chalky plastic! The biggest difference I can see if the chalky plastic will have a little bit of a shine to it, while the basecoated models are usually very matte. My QH Yearlings and clydesdale foals are definitely molded out of this kind of plastic. If you scratch the surface on the bottom of their hooves you can tell there is no paint there. This chalky plastic Running Stallion was broken in shipping. You can see the plastic almost looks like plaster all the way through. It is known to be much more brittle than normal cellulose acetate.

Below is a photo of a chalky plastic Western Prancer with a normal plastic prancer. You can see here how the mold detail really pops out, unlike what we saw with basecoat chalky models, which often lose detail with that thick extra coat of paint.
How much is my chalky model worth?
In general, chalky models carry a higher value than their normal plastic counterparts. In some cases the difference in value can be huge, and in other cases only a few dollars. I am working on compiling a trade history of known chalky models and hope to one day have a relatively accurate value table on the site. There are several factors involved, though, as they would be in the value of any Breyer model.
First, is it a popular mold? The Proud Arabian Mare and Foal, Indian Pony, Adios and the Fighting Stallion are among the most popular of Breyer's older molds, and so it is no surprise that these chalky models carry an extra premium. The Family Arabian molds, on the other hand, are less desirable and so the chalky versions generally sell for only a small amount more than the standard issue Family Arabs (which isn't very much to begin with). These would be a good place to start a collection!
Second, how rare is it? All chalky models are relatively scarce, but some moreso than others. Chalky Clydesdale Foals come up for sale somewhat frequently, while chalky Misty of Chincoteague is hardly ever seen for sale. The harder to find models will command a much higher price than the ones that are more available.
Third, and more unique to chalky models, how much white does the model have? While I personally think my chalky Justin Morgan is cool, he doesn't really stand out among chalkies because he has no white markings. You really have to look closely to even tell he is chalky. The chalky models with less white will tend to have lower values (also not helped by their happening to be less popular molds) with additional examples being the Nursing Mare & Foal, solid bay Jumping Horse, and Man O War. On the other hand, the all alabaster chalky models are very popular and highly sought after.