Why can one chlorine atom help produce many chloromethane molecules?

The production of many chloromethane molecules from a single chlorine atom is possible because the process is a chain reaction.12

In this mechanism, the chlorine atom acts as a transient intermediate that is consumed in one step but regenerated in another, allowing it to facilitate multiple reaction cycles. The process follows these propagation steps:1

• A chlorine atom ($·\text{Cl}$) reacts with a methane molecule (${\text{CH}}_4$) to produce a methyl radical ($·{\text{CH}}_3$) and hydrogen chloride ($\text{HCl}$).2
• The resulting methyl radical then reacts with a chlorine molecule (${\text{Cl}}_2$) to form the product, chloromethane (${\text{CH}}_3\text{Cl}$), and a new chlorine atom ($·\text{Cl}$).2

Because the chlorine atom is regenerated in the second step, it is free to collide with another methane molecule and repeat the cycle. This sequence continues until a termination step occurs—such as the combination of two radicals—which breaks the chain. This efficient regeneration is why a single act of initiation can result in the production of many molecules of the final product.123