Hi Chris,

Thank you for contacting Mearto with your appraisal inquiry.
It's difficult to precisely date this chair because the woods, design and methods of construction are all ones that have been used since the mid 19th Century (circa 1850).
Regrettably, children's wood high chairs are a very soft aspect of the furniture market, with even signed, labeled and documented examples bringing very little money; in the case of this chair, it's worth $50-75.
Based on the photos and information provided, and subject to examination, this is:

An antique or vintage child's walnut high chair
probably American, mid 19th Century to early 20th Century
With shaped tablet crest raised on turned stiles and spindles, curved arms over a plank seat, raised on four turned legs, the front ones joined by a footrest and a turned stretcher. Unsigned.
Overall height: 38 inches' width across seat: 13 inches; depth of seat: 11 inches
CONDITION: This high chair appears to be in generally good condition with wear commensurate to age and use.
PROVENANCE: Inherited
$ 50-75*
*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