I have a fireplace in the living room with a standard fireplace, not insert.  The chimney part is just a metal pipe running up and out of the roof.  

The issue is the walls around the fireplace fill a cavity that is probably about 6 -8 ft long and 3-4 ft wide.  The top of the cavity in the attic is completely open with the metal exhaust pipe coming up and out the attic.  The walls around the chimney are nothing but sheetrock (pretty sure I didn't see insulation on them).  I live in south texas where the attic is hot as hell and all that hot air fills that cavity and causes the walls to stay pretty warm.  

Is there a proper way to either insulate the walls, or close off that air gap and seal around the chimney pipe?  I don't use the fire place whatsoever, but if I sell the house, I don't want it to be against any fire code or be a hazard.

I can't tell you code or proper ways to do things.  

This is what was installed at my place last year--functional chimney on a wood stove.  Blown in cellulose ceiling insulation goes right to that box.

So not really what you're after, but it drastically reduces the uninsulated space you currently have

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Is the fireplace chimney chase large enough for you to drop down inside on both sides?  If so, you can get someone to spray closed cell foam in the stud cavities or try to do it yourself. As long as you maintain 3” distance from the flue and firebox (code is 2” but just to be safe because foam will reach combustion temps around 650 degrees) you should be fine.  Another way would be to add a layer of 3/4” plywood around the top of the chase where it meets the attic and then a layer of foam board or lay down some batts, again keeping that 3” gap.

I assume by  "attic" you mean an area above the  occupied spaces that is NOT used / occupied and is  unfinished?  That space should be VERY  well ventilated.  You want vents down low in the eves, LOTS of them, and make sure they have open channels  to  space around the insulation,   and then  a  ridge vent system or LOTS  of  roof vents  and large end gable vents.  

So far as the chimney, you must investigate EXACTLY   what that vent  (chimney) is  and find out the  "clearance to combustible"  specs.   Normally these  metal chimneys are required to be  (for wood fires)  "class a"  as opposed to  "B or C" for gas,  and there is ALWAYS  a specification  for fire clearance to combustibules.   May be  1"  or more, or less.  I have not kept up with  recent changes, there even may be some that is  "zero" clearance.  But you MUST find that out

You may  want to  get  sheet metal/ someone  to build  a cylinder around the pipe to keep  insulation away from it.

Is it too big to fill?  Is it large enough to get down in there and install  wall insulation?  Open it up someplace below,  might even  build a crawl access into the chimney area?   What you describe  sounds  pretty big?

We just use friction fit batt insulation in stud cavities in the chase of the fp.

We need pictures. There are no one-size-fits-all wood stove/fireplace installations and it's not somewhere you want to guess, cut corners, or mess up.

I'll try and get some on my next days off.  It is probably big enough for me to drop down into it.  Now, getting out might be fun.  

There is a hallway/bedroom behind it so it might be possible to cut a little door into the wall.  

I don't plan on messing with it until winter.  It's just too dang hot to get in the attic to work during the summer down here.