Only if you want to include thirteen-year-olds in Finland in your conversation. The whole point of local chat is that it's local. If you have a good chat, you can pick up your laptop, walk a few feet, and have a real conversation.
This might not be the best implementation of the idea, but it's a start. Imagine a coffee shop with a chat room just for that coffee shop. You could post an away message of what you're reading, and if someone was interested they'd send you a message. You could meet one or two people every single time you went there. Technology would finally bring people together instead of driving them apart.
Or imagine if your neighborhood had a chat room or bulletin board. I don't know any of the other people in my neighborhood. It would be great if I could let them know when we are cooking, so they could come and hang out and have a bite with me and my roommates. However, how do I find them? Where can I post that information where 15-year-old Singaporans aren't also in the conversation? I want to communicate only with a narrow, local subset of humanity here.
The only people today that are doing local social software are Craigslist and dating sites. Both of them bring real people together in real life. However, there is room for more applications in the space.