It is a double-ended kayak paddle with a chainsaw duct-taped to each end. It is made by combining a paddle and a chainsaw. It is a heavy weapon and cannot be stored in Chuck's inventory.
This combo weapon has been described as:
"Remember Donatello's bo staff from "Ninja Turtles"? Well, imagine if there was a running chainsaw at each end. Suddenly Donatello seems a lot less bad ass."[1]
Skorge using the Dual Chainsaw Staff, possibly inspired the Paddlesaw.
The Paddlesaw has very high durability and attack damage.
According to the Making of documentary, the Paddlesaw was one of the first combo weapons to be designed by the development team. It was also one of the first combo weapons ever shown, aside from the Slicecycle.
In an advertisement in the October 2010 Official Xbox Magazine, the paddlesaw is shown with a different appearance; the chainsaws are dark blue and the paddle is wooden.
The weapon is possibly a reference to, or possibly inspired by, the Dual Chainsaw Staff wielded by Skorge, in the "Gears of War 2" game.
Chuck holds the weapon differently in game than on the box art, holding it like a spear rather than like a paddle.
In the items.txt PC game files this weapon has the name "Combo_Paddlesaw"