A process and apparatus for continuously depositing a coating on a fibrous material. The process is a chemical vapor deposition process that includes causing multiple strands of a fibrous material to continuously travel through a coating zone within an enclosed chamber defined by a housing so that portions of the strands contact a reactant gas as the portions travel through the chamber, directly heating the portions of the strands without physically contacting the strands and without directly heating the housing, and depositing a coating material on the strands as a result of the reactant gas contacting the portions of the strands and decomposing to form a coating of the coating material. Heating of the strands can be achieved by capacitive coupling, inductive coupling, microwave radiation, and radiant heating.