Hi Jeffrey,

Thank you for contacting Mearto with your appraisal inquiry.
While Carlo Bugatti did make chairs with circular backs, those he did all had a different "curule" or X-form base.
This chair was made in the late 19th Century (roughly circa 1870-1900) during the "Renaissance Revival" period, when, in a response/backlash to more modern designs of the Aesthetic movement prompted a nostalgia for historical aesthetics and design. Unfortunately, this style is not enjoying very high popularity at the moment and, with less demand than supply, values are low.
Based on the photos and information provided, and subject to examination, this is:

An antique Renaissance Revival style carved and turned walnut armchair
unattributed maker, probably English or European, late 19th Century
With a circular carved and pierced back with acanthus motifs issuing turned arms raised on bulbous supports over a trapezoidal seat with inset yellow (silk?) upholstery with brass tack trim, raised on flaring turned legs joined by a barley-twist X-stretcher. Unsigned.
39 inches high, 24 inches wide
CONDITION: Not examined in person; wear appears to be commensurate with age and use.
PROVENANCE: Inherited
$ 100-150*
*represents a fair-market value for auction purposes; retail or asking price may vary.

Please let us know if you have additional items to appraise, or questions/concerns, and thank you again for using Mearto.
~ Delia