The chairs in the image are a style known as "Gainsborough chairs" or "Gainsborough library chairs." While the original Gainsborough chairs were designed by Giles Grendey in the 18th century, this style has been widely reproduced and reinterpreted by many furniture manufacturers over the centuries. 
Based on the appearance of the chairs and information from various sources, these specific chairs may have been manufactured by a company producing furniture in the classic style. One potential manufacturer known for producing chairs in the Gainsborough style is the Hickory Chair Furniture Company.