The decision of which side to wear a wallet chain is largely a matter of personal preference and style. There is no hard and fast rule dictating the specific side on which a wallet chain should be worn. However, there are some common practices and considerations that may influence one's choice.
Traditionally, many individuals wear a wallet chain on the same side as their dominant hand. For example, right-handed individuals often opt to attach the wallet chain to the right side of their pants or belt loop. This placement allows for easier access to the wallet and adds a sense of balance to the overall look.
Another factor that may influence the choice of side is the individual's preferred pocket for carrying their wallet. If someone usually keeps their wallet in their back pocket, they may choose to attach the wallet chain on the corresponding side for convenience and ease of use. On the other hand, if someone prefers the front pocket, they might choose to wear the chain on the same side to maintain a symmetrical appearance. 
It's worth noting that the placement of a wallet chain can also be influenced by fashion trends and subcultural influences. In the past, punk rockers and skateboarders often wore wallet chains on either side, reflecting their rebellious and nonconformist attitudes. This approach was less about practicality and more about making a bold fashion statement.
Ultimately, the decision on which side to wear a wallet chain rests with the individual. It's an opportunity for self-expression and personal style. Some may prefer a more traditional or balanced approach, while others may embrace asymmetry or nonconformity. The key is to wear the wallet chain in a way that feels comfortable and reflects one's unique fashion sensibilities.