NEW YORK, United States — J. Crew Group Inc. plans to spin off its Madewell denim chain in a public offering, the company announced in a filing Friday, five months after announcing it was considering such a move.The number of shares to be offered and the price range for the proposed offering haven’t yet been determined, according to the filing. Chinos Holdings Inc., which owns J. Crew, expects to use any proceeds to pay down debt and for general corporate purposes.Madewell would follow Levi Strauss & Co. as the next denim company to tap public markets. It will have to gauge investor demand, however, as most apparel retailers' shares have lost value this year. In J. Crew's case, however, debt-related needs may take precedence over timing.“The IPO could garner a substantial valuation and help pay down a meaningful portion of the over $1.7 billion in debt,” said Raya Sokolyanska, an analyst at Moody’s Investors Service. “But the ultimate ability to address J. Crew’s highly leveraged capital structure depends on the public market’s receptivity to apparel retailers and the company’s operating performance.”Chinos will be renamed Madewell Group Inc. before the IPO is completed, the company said.By Lisa Wolfson; Editor: Anne Riley Moffat.