Remove Chimney to save heat loss?
 

My 4' x 3' chimney serves no purpose and I would like to remove it. I also have heard that you can loose a lot of heat through this "pipe" in the winter. Anyone done this and or know of anyone who has? I have never done any brick work, but I assume I can just chip away at the mortar joints and pull each brick off one by one? Any brick layers/removers out there have any input? Thanks in advance.

A 5 pound hammer and a 3 inch chisel should make short work of this job. You could also stukk insulation in the flue.

I don't have a flue, I don't have a fireplace. The chimney goes from my basement to the roof. It about 30 ft tall from its base. I really only want to remove about 8 ft of it for now.

You can often rent "Chip Hammers" more or less a hammer drill that has a hammer only setting, it works like a hand held jack hammer.
Don't toss the bricks down the center of the chimney, they can get wedged in and cause cracks, they also make the chimney useless if you later realize you need it, if you do realize you need it the ideal way to update it is to run stainless double wall chimney pipe from the attic up and out, but for now just knock the brick down level with the attic, seal it and insulate it, don't forget the air sealing!

Leaving the brick chimney in the house does take up space, but it also is a thermal mass that will help regulate the indoor temperature, if you later want to run anything from the attic to the basement, like solar hot water or solar electric lines, you will have a nice clear run as well.

I would rent or Buy a rotary hammer (or as Ryland knows it a chip hammer)
as Ryland suggested , and make short work of the motor joints.
The Professional demo tool is called a rotary hammer and not a hammer drill which is much cheaper/lighter/weaker/slower

A rotary hammer will turn concrete / motor into dust in 1 second , wear a dust mask !

They are lighting fast and can be had for cheap (harbor freight for instance).

I bet this would work well. I have one but have only drilled with it but is works very well.
harbor freight hammer drills - YouTube
Maybe get the extended warranty and look up a 20% off coupon.

$78
10 Amp 3-in-1 1-1/8 in. Variable Speed SDS Rotary Hammer

Maybe a Pawn shop has one for $50

I have the Dewalt WD511 , 7.8 amp hammer drill (not the rotary hammer) I bought off eBay for $50 , works great for drilling in concrete, it has drill or hammer and drill but does not have the hammer only mode.

An old chimney will come apart remarkably easy. I had the roofers remove the outside parts when my house was re-roofed. I remove 6-7 feet of chimney in the attic. It came apart with a 20oz hammer.

The hardest part was carrying all those bricks down two flights of stairs in 5 gallon pails.

Wouldn't it be easier just to seal it off?

You could repurpose it to warm the basement with attic air in the winter. A few members have done just this, and have proven the concept.