Whether you use a western curb bit like the grazing bit, Tom Thumb or the various correction bits, or an English curb bit such as a kimblewick, pelham or the curb bit of a double bridle, it is important that it always be used with a curb chain or strap. Some driving bits like the Liverpool are curb bits, and many hackamores have shanks, and they too, should be used with a curb chain or strap. The curb chain or strap looks fairly insignificant on a bit, but it's essential to ensure that the bit is both effective and comfortable for the horse.
Often, curb chains are used on English bits and bridles, while straps are more commonly used on western bits. However, both straps and chains are available for either. A strap, whether it is made of leather or synthetic, is the mildest form of curb strap. Chains come in varying link sizes and thicknesses and there are many different types of chains available.
The finer chains may be used for horses that are pullers, but for general riding, a strap or medium-linked chain is sufficient. Regardless of the thickness of the chain, they should always be turned so that they are laying flat, like a watch band. This might take a few turns to get a tangled chain flattened out. One end of the chain on an English bridle will be left on the right hook attached to the bit. Once the bridle is on the horse, you turn the chain until it is flat and even, and then hook it onto the left chain. The right hook is commonly squeezed closed, so the chain doesn't fall off. There is also a larger center link that a "lip strap" can be threaded through. The lip strap prevents the horse from grabbing the bit shanks and keeps the chain from detaching if it comes unhooked. Leather English curb straps will have a few links of chain on each end of the leather portion, so they can be done up exactly like the chains.
Unlike the hooks on English curb chains, western chains fasten on the bit with a leather strap and buckle on each side. The leather straps will have holes, so they can be adjusted similarly to a belt. There isn't a link for a lip strap because many western bits have a shank hobble or slobber bar that works in a similar fashion.
A snaffle bit only places pressure on the bars of the horse's mouth when you pull on the reins. However, more happens when you pull on the reins of a curb bit. As the shanks are pulled backward, the horse will feel pressure on the top of its head (poll), the bars of its mouth and in the chin groove where the strap or chain is sitting. The curb strap prevents the bit from rotating too far in the horse's mouth, which may be very uncomfortable, especially if there is a large spoon or port on the mouthpiece of the bit. The curb chain limits the pressure on the upper palate of the horse's mouth as the mouthpiece rotates. The pressure under the chin also pulls the bit down against the bars of the horse's mouth, amplifying the rein aids.
Proper adjustment of the curb chain is very important. If the curb chain is too tight, there will be constant uncomfortable pressure on the horse's chin groove and bars of the mouth. The rein aids will be exaggerated, which could cause the horse to toss its head or open its mouth to escape the pressure.
If the chain or strap is too loose or left off altogether the leverage action of the bit won't be as effective. If there is a port or spoon on the bit, it can be pulled against the roof of the horse’s mouth sharply, causing the horse pain. The curb strap or chain should be done up so that when the reins are pulled, the shanks of the bit don't rotate beyond 45 degrees. Many people use the width of two fingers between the horse's chin groove and the strap or chain to estimate how tight the chain is. This is only an approximation after you've checked that the shanks will rotate about 45 degrees.
So, always use a curb strap or a chain. It may look small, but it's an important part of your horse's bridle.