FYI: I'm not an expert on old stoves. (btw: looks like you got a STEAL on that!)
It appears to be a Parlor stove.
I'm assuming that decorative chrome top comes off...? (Since you mentioned 'cooking beans' ) Because my thought was that the piece you're asking about was some type of hot plate, and another piece -like a handle that inserts into that small hole on the back of it- would go there so it could be moved around.
I'm also going to assume that the door is on the right side of that photo...? ...maybe a part for the damper (air in-take -- assuming the air in-take is from underneath)?
Just guessing, and I'm not even there to look at it.
Installing a chimney isn't that big of a deal. The hardest part is cutting the hole into the roof and ceiling... making sure they're lined up.
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What does it say on the front? L - vec?
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) Because my thought was that the piece you're asking about was some type of hot plate, and another piece -like a handle that inserts into that small hole on the back of it- would go there so it could be moved around. 
Scored me a 'Franklin' with just one 'Benjamin' on Craigslist
