White chalk

We will reach out to some of our drawing experts to provide you with additional information but chalk “of the old masters” was typically derived from calcium carbonate (limestone) deposits found in Northern Europe. This white powder-like substance was (and still is) collected from these white cliffs and quarries that were formed from the fossilized remains of tiny sea creatures that were millions of years old. The limestone can be further cleaned and refined of impurities to produce a very fine powder, made into a wet paste, which then was traditionally bound into a stick using a small amount of adhesive such as animal skin glue or some type of gum (e.g. gum arabic or gum tragacanth). Today I believe it is more common to find methyl cellulose binders in white chalk but again our experts can correct me if I am wrong on that. An excellent book on drawing materials used by the Old Masters is “The Craft of Old-Master Drawings” by James Watrus (2002, Madison: University of Wisconsin Press). As for lightfastness, I would be very surprised to find whether there are issues regarding white charcoal pencils so I would not be especially worried about that.

Kristin covered most of the issues here. The Watrous book is very useful and relatively cheap. We heartily recommend it for those interested in Western drawing materials.
The Old Masters generally used three colors of chalk, red, black, and white. Natural yellow chalks (lumps of yellow ochre) were sometimes used starting about the 1500s but were far less common. The red chalk is essentially lumps of red earth colored by the presence of iron oxide and the black chalk is slate colored black by the presence of carbon.
There were two types of natural white chalks mentioned in the early literature (Cennini, etc). The most familiar and useful for the artist were natural lumps of calcite or steatite (calcium carbonate) and the other from soapstone, which is a hydrated magnesium silicate. The later was recommended for use on fabric and continues to be used for that purpose under the name of “tailor’s chalk”.  All of these materials were simply dug from the ground and cut into a usable shape. Additionally, all of them are, and continue to be, eminently lightfast.
Sometime in the 1500s artists and artisans began to make fabricated chalks. These are similar to what we now call pastels. They were made by mixing pigments, with or without fillers like calcium carbonate, with a binder of the appropriate strength (glue, gum, etc) to create a chalk of the right resiliency for the purpose at hand. Natural chalks continued to be used, especially in the above three colors, along with the fabricated chalks making it difficult to determine which was used on a particular drawing without very sophisticated chemical analysis.
Probably, natural white chalks were the norm until relatively recently since the raw material is so abundant. Having said this, modern fabricated white chalks, made for fine art purposes as opposed to chalkboards, should be perfectly suitable in terms of lightfastness. The issue become a little more complicated when you are talking about colored chalks where the lightfastness of the pigment comes into play. For these, and like all fine art materials, one should only use professional grade supplies created from stable materials.
If you are interested in experimenting with the historical material, I see that you can get natural white chalk sticks from a few sources including on Amazon.com and Kremer pigments.