A process for converting a crude glycerol, crude mixtures of naturally derived multihydroxylated-aliphatic hydrocarbons or esters thereof to a chlorohydrin, by contacting the crude glycerol, crude mixtures of naturally derived multihydroxylated-aliphatic hydrocarbons or esters thereof starting material with a source of a superatmospheric partial pressure of hydrogen chloride for a sufficient time and at a sufficient temperature, and wherein such contracting step is carried out without substantial removal of water, to produce the desired chlorohydrin product; wherein the desired product or products can be made in high yield without substantial formation of undesired overchlorinated byproducts; wherein said crude glycerol, said ester of crude glycerol, or mixture thereof is derived from a renewable raw material. Chlorohydrins made by the process of the present invention are useful in preparing epoxides such as epichlorohydrins.