AltAssets revealed in March that the company was seeking up to $200m from selling the 10 million shares.
Bain bought Trinseo, then known as Styron, from chemicals giant Dow Chemical for $1.63bn in 2010.
In January Trinseo sold $1.3bn of high yield bonds to help pay down its debt.
According to its most recent quarterly results, the company saw revenue drop six per cent against the previous year to $1.245bn, though EBITDA grew 113 per cent to $104m.
The proceeds of the listing will go towards debt, working capital and “general corporate purposes”, the company said.
Trinseo previously planned a public listing in June 2011, but later withdrew.
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