A bumper crowd watched visiting goalkeeper Christian Puggioni stand firm against the few serious chances the home side enjoyed, with Antonio Mirante the far busier man between the sticks.
But Puggioni would guarantee the points were shared with his late one-handed stop on a Jonathan Biabiany header.
All eyes were on Antonio Cassano, a high-profile summer capture from Inter Milan, but it was Amauri who enjoyed the first chance after being put through by Marco Parolo.
Puggioni cleared without too much difficulty and Chievo raced down the other end to test Mirante through Gennaro Sardo.
The Gialloblu came close in the 20th minute, Cyril Thereau forcing quick reflexes from Mirante when he tried to follow up Perparim Hetemaj's strike against a post.
Mirante's third save was the most impressive as Alberto Paloschi tried his luck when one-on-one with the Parma keeper, who swept the ball away with his legs.
Parma needed some inspiration to gain a foothold in the game and they found it through Cassano, whose clever ball to Marco Marchionni was only kept out of the net by the covering Boukary Drame.
There was nothing to separate the two sides at half-time, however, with tame shots from Cassano and Jaime Valdes offering Puggioni some catching practice.
Amauri came knocking again on the hour mark but his shot from Cassano's short cross sailed wide, before Paloschi saw an effort blocked by Mirante at the other end.
Debutant Alessio Sestu picked his spot from way out but missed as time ticked away and Parma would have no better chance than when Biabany headed Cassano's corner against Puggioni's outstretched glove.