Lynx (including bobcats), Cougar
Lynx spp and Puma Concolor
*Lynx up to 66 pounds and over 4 feet long (in North America, the species are smaller, up to 30 pounds and 41 inches)
*Cougars can be up to 220 pounds and up to 9 feet long (including the tail)
Both lynx and cougars are large felines, and can have large paws for their relative size. Lynx have short tails, while the cougar's is long. Various lynx species may be generally golden or pale in color. Their fur may be plain or spotted, and they have lighter fur on the chest, stomach and insides of the legs. They have tufts on the tips of their ears, and a ruff of long fur around their necks, giving them fluffy-looking cheeks. By contrast, cougars typically have a plain coat, tawny colored with white on the muzzle.
Cougars are typically found in parts of western North America (and a small part of Florida), and in South America. Various lynx species are found in North America, Europe and Asia.
Lynx and cougars are uncommon predators of chickens in urban and suburban areas, so you are unlikely to have predation by these creatures unless you live rurally. Cougars especially tend to avoid areas of human habitation, but there are always exceptions, and bobcats can sometimes make incursions.
In most cases, you will not find remains if the predator is a cougar or lynx; your chickens will simply be carried off. They will normally not kill more than they will eat, but again, there have been some exceptions.
If that is the case, it will be hard to differentiate between a kill by dogs or a kill by large, wild cats like lynx and cougars... unless you either see the predator or spot tracks. However, when they do kill more than they can eat, both types of cat will often shallowly cover uneaten remains with snow, dirt, leaves or other detritus in a safe place to come back to and feed on again later. If you find such a spot, cougars can reach out and scrape about two feet away to cover the remains, while the smaller bobcats will scrape out only about 15 inches at most.
Protecting Your Flock
To protect your birds, double check that any wire mesh on your coop is securely attached. If they want in, like other large predators, lynx and cougars can simply muscle through areas with weak points. They can leap very high (bobcats can leap 6 feet), and are good climbers--they can climb fence posts to get over fences and can even climb your wooden coop directly to find entry near the roof. To exclude them, be sure your fence is strong and tall. They don't normally dig to get to their prey, but if it's the only way in, they certainly may try it! Bobcats in particular don't need much space to squeeze in, only a few inches in some cases.
If the openings in your fence are large enough, these big cats can reach through with paws and claws to snag your chickens and pull them out. For that reason, you will want to use a fine mesh hardware cloth (usually 1/2" or 1/4") to fence your run, and the only way to be sure they don't get in will be to have it enclosed entirely, top and bottom both.
Remember: don't use chicken wire for your coop or run: chicken wire is not a barrier to predators. Lynx, cougars and other predators can tear right through it like tissue paper. Chicken wire should only be used to keep chickens in, not to keep predators out, so use welded wire hardware cloth.