What are those tasty glands that are in chicken thighs?
You mean the spongy red stuff that turns gray when you cook it, that’s in the big thighs, the ones that have part of the back attached?
I believe those are the remnants of air sacs.
http://www.fsis.usda.gov/OFO/HRDS/SLAUGH/airsac/airsac1.html
Chicken Glands??? BAND NAME!!! 
Air sacs? “There is no gas exchange with the blood in these vessels.” What do they do?
Reduce body weight and help the chicken fly?
I much prefer DDG’s answer to the “anal scent glands” I was expecting.
TMI–do not read if you really like those “tasty glands”:
Dunno what they do, because after a quick cruise through Google, and after seeing all the hits that have to do with ghastly chicken diseases that apparently afflict those “chicken air sacs”, I have suddenly become sidetracked into resolving never to eat those tasty glands again.
And I don’t really wanna talk about them any more, either…
I was hoping I wouldn’t have to answer this one. (sigh) Technical mode ON!
The respiratory system of the chicken is not like ours. Our main trachea splits into a left and right mainstem bronchus (one for each lung, which split and re-split (typically 12 levels deep) in a tree-like fashion before dead-ending in “terminal alveoli” (air sacs). All but a few human alveoli are dead ends.
In the chicken, the trachea splits into two primary bronchi, called mesobronchi, which pass through the lungs to the abdominal air sacs. Secondary bronchi branch from the primary bronchi and go to the other air sacs. From the secondary bronchi, tertiary bronchi (parabronchi) branch and anastomose (join together, allowing air to floe betwen them). From the tertiary bronchi a network of thin walled tubes (air capillaries) are in intimate contact with blood capillaries allowing gaseous exchange. There are no dead end alveoli.
In man, gas exchange takes place solely in the walls of the alveoli, heavily infiltrated with specialized capilaries. In the chicken, gas exchange also takes place in tubules along the way. This more efficient gas exchange is one reason why birds are more susceptible to anaesthetics and gaseous toxins than mammals are. Think “canary in a coal mine.”
Flying birds make heavy respiratory demands. They usually have a higher resting metabolism (per kilogram) and higher body temp than mammals. In flight, their metabolic rate is higher than any mammal can sustain. This means they need more air (per kilogram) and need it continuously. During flight, the thoracic skeleton is fully engaged in the act of beating the wings, and this full-body motion, typically on the rough order of one per second except during take-off or landing, would interfere with or preclude rapid breathing
A resting human typically breathes 12-20 times a minute, during heavy exertion this can go to 40 or more, but it becomes difficult to breath effectively at above 60. The lungs simply can’t fill and empty effectively that rapidly. Tthe elasticity of the tissues isn’t optimized for it, and the exertion of rapid forced breathing becomes a losing proposition. Breathe too fast, and you burn more than you gain, and you exhaust you primary and accessory muscles of respiration.
Flying birds (from which the chicken evolved) circulate air through their interconnected respiratory system, rather than filling and emptying their lungs like balloons. The air sacs are also believed to act as reservoirs of air between breaths, and probably pre-condition (humidify and warm) the rapidly moving air much as our sinuses do. Like our sinuses, they are a point of initial contact with the outside environment, and are prone to infection or inflammation.
Air also enters the bones. A bird’s air-filled skull, humerus, clavicle, heel, and lumbar and sacral vertebrae help keep its weight down.
Linky for more information on the comparative anatomy and physiology of birds
However, the skeleton of a chicken (scroll to the bottom) often fools people (even undergraduate students in comparative anatomy during practical exams). If I correctly understand the structures indicated by the OP, they are in the the femoro-pelvic joint, corresponding to the ‘ball and socket’ acetabulum of our own hips.
There are no air sacs in that region. The ‘glands’ also appear too dense to be air sacs, which are removed during the course of gutting the chicken in any case. I believe these are synovia. A synovium is a “lubricating sac” of durable but soft connective tissue, filled with a lubricating fluid (which helps sustain the synovial tussues). It’s function is to separate, cushion, and lubricate the cartilage at the end of the bones of major joints.
If you’ve ever seen arthoscopic images of, say, your knee, you’ve looked inside your synovium. This is also where the uric acid crystals of gout often form. In rheumatoid arthritis, the synovia can become so chronically inflamed that it thickens and hangs loose outside the joint like saddle bags. This is called “pannus” (Latin: “saddle bag”) - a term that also describes other, very differnt structures, like the overhanging fat of a paunchy human abdomen.
Dammit, Jim, I’m a doctor, not some quack! Corrections on bird anatomy and physiology would be most eagerly welcome.
Mmmmmmm … chicken glands. 
^^ Oops. I meant to say “I’m a quack, not a duck doctor”
Are you sure they are in fact glands? There are two types of muscle fibre… and they look different. Might you just not be seeing those?
I’m sorry if I gave the wrong impression. Synovia, like many tissues, exude a fluid, but are not glands. The structure I’m speaking of does not appear to have much muscle fiber, and isn’t strongly anchored to a bone, as you’d expect a skeletal muscle to be. It’s lies loosely within hollow in the bone - specifically (per the chicken skeleton diagram linked above) in a broad shallow socket where the femur (thigh bone) meets the chicken’s equivalent of a pelvis.
There is some muscle fiber in that region. You can see why muscles could be useful in controlling such a loose pelvic joint (compared to our own deep socket acetabulum). Chickens are just as bipedal as we are, but their lower mass/volume ratio allows a looser joint.
You can also see why you wouldn’t want to put a gland (or anything else unrelated to the joint) between the thigh bone and the socket it sits in: the arrangement is essentially a natural mortar and pestle.
I called them glands because I didn’t know what they were.