Step 1: Understand what a hydrate is and factors influencing hydrate formation.
A hydrate is a compound that contains water molecules associated with its crystal lattice. The ability of a salt to form a hydrate is primarily determined by the polarizing power and charge density of its cation. Smaller cations with higher charges (i.e., higher charge density) have a stronger electrostatic attraction for the polar water molecules, leading to the formation of stable hydrates.
Step 2: Analyze each given chloride based on its cation's properties.
MgCl\(_2\): The cation is Mg\(^{2+}\). Magnesium is an alkaline earth metal (Group 2). Mg\(^{2+}\) is a relatively small ion with a +2 charge, giving it a high charge density. This allows it to strongly attract water molecules, and it commonly forms hydrates such as MgCl\(_2 \cdot 6\operatorname{H}_2\operatorname{O}\). Therefore, MgCl\(_2\) exists as a hydrate.
CaCl\(_2\): The cation is Ca\(^{2+}\). Calcium is also an alkaline earth metal. Ca\(^{2+}\) is larger than Mg\(^{2+}\) but still has a +2 charge. It is well-known for its hygroscopic and deliquescent properties and readily forms hydrates, such as CaCl\(_2 \cdot 6\operatorname{H}_2\operatorname{O}\). It is often used as a desiccant. Therefore, CaCl\(_2\) exists as a hydrate.
LiCl: The cation is Li\(^{+}\). Lithium is an alkali metal (Group 1). Li\(^{+}\) is the smallest cation among all alkali metals. Its very small size and +1 charge result in an exceptionally high charge density for a Group 1 ion. This strong polarizing power allows it to attract water molecules strongly, and it forms hydrates like LiCl\(_\cdot \operatorname{H}_2\operatorname{O}\) or LiCl\(_\cdot 2\operatorname{H}_2\operatorname{O}\). Therefore, LiCl exists as a hydrate.
KCl: The cation is K\(^{+}\). Potassium is an alkali metal, but K\(^{+}\) is significantly larger than Li\(^{+}\), Mg\(^{2+}\), or Ca\(^{2+}\). Due to its large ionic radius and relatively low charge density, K\(^{+}\) has a very weak ability to attract and bind water molecules to form stable hydrates under normal conditions. While it might absorb some moisture from the atmosphere, it does not typically form a definite, stable hydrate. Therefore, KCl generally does not exist as a hydrate.
Step 3: Conclude the chloride that does not exist as a hydrate.
Based on the analysis, KCl is the chloride that does not exist as a stable hydrate under normal conditions due to the large size and low charge density of the K\(^{+}\) cation.
The final answer is \( \boxed{\text{KCl}} \).