If the chair came with a written limited warranty (and most new products are sold with some sort of written warranty), then pursuant to the federal Magnuson-Moss Warranty Act
(15 U.S.C. 2308), during the term of that written warranty, the manufacturer must also honor the Uniform Commercial Code implied warranty of merchantability.
TX Bus. & Comm. Code 2.314.
The warranty of merchantability requires that: "Goods to be merchantable must be at least such as (1) pass without objection in the trade under the contract
description; and (2) in the case of fungible goods, are of fair average quality within the description; and (3) are fit for the ordinary purposes for which such goods are used; and (4) run, within the variations permitted by the agreement, of even kind, quality and quantity within each unit and among all units involved; and (5) are adequately contained, packaged, and labeled as the agreement may require; and (6) conform to the promises or affirmations of fact made on the container or label if any."
A chair which repeatedly falls apart is not merchantable, therefore, you are entitled to sue for damages for the value of the chair that you should have received, or the reasonable cost of a replacement chair from a different manufacturer.
So, the answer to your question is an unqualified, "yes." You can sue the manufacturer and the vendor/seller for breach of the implied warranty of merchantability.
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