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Chievo were content to wait for chances to break on the counter, a tactic that nearly paid dividends after 17 minutes as Marcelo Estigarribia forced Christian Abbitati to make a fine stop with a powerful drive from distance.
The Flying Donkeys were presented with a glorious chance to break the deadlock soon after, but Bostjan Cesar could not direct his header towards goal despite being left unmarked at the far post.
Milan struggled to create clear-cut chances despite controlling possession and territory, with Andrea Poli flashing wide just before the break for the visitors.
Robinho went by far the closest to breaking the deadlock with time running out, striking the post from close range with time to pick his spot.
Montolivo was dismissed soon after but there was still time for Alessandro Matri to spurn a late chance, before Sergio Pellissier saw red in stoppage time for arguing with the referee as a scrappy affair ended in stalemate.