There's a couple of things here. What noises are bothering you? If it's discussion - is the volume at a tolerable level and you're just being a little irritable, or are they talking at a higher tone and it's disruptive to everyone?
You've isolated the situation to 2-3 people - that leaves ~5 others that may have the same feelings as you. Have you discussed with anyone else if they have a difficult time focusing when others are having conversation? It's highly reasonable to have this talk with one of your peers, especially if it's interfering with your productivity.
Have you tried bringing headphones and listening to music (It doesn't have to be music you hear on the radio. It could be instrumental, for example)?
As for the chat piece of this discussion - there are plenty of companies that utilize this. Whether it be Pandion, or any other vendor - these are common. Do not feel shy or vulnerable for asking if people in your workplace utilize these.
At a point when you feel like you've expensed all other routes, I would discuss with your manager that your work is optimized when the atmosphere is less-noisy, and it has been hard to concentrate with constant discussion going on around you and it's at a volume which disrupts your work. Is there an option for you to be re-located? Your manager should find a way to help you with the problem while keeping a balance in the workplace.