If you need quiet time all day long to get any work done you'll be hard pressed to find a good solution. You might want to consider looking for a different kind of job that allows you to sit on your own but those jobs have their own difficulties.
Given that statement, let's see what you can do to mitigate the problem. Preferably try to combine as many options as possible to maximise their effectiveness.
1) Talk with your superior. Make sure they are aware that noise is an issue for you and that your productivity will not be as high as it could be. Try to work with them to reduce the issue where possible.
2) Drown out the chatter with less-distracting noise instead. If my coworkers are chatting too much at a time I need to focus I put on some instrumental music loud enough so I cannot understand what they're saying anymore. I'm slightly distracted and might humn along with the songs a little bit, but it's far better than automaticaly trying to understand what they're saying.
3) If you have flexible hours, try shifting your workday. Either earlier or later, not both like your third solution (as you've seen, that doesn't work). If you shift it earlier, try to get the most important high-focus things done before chatty coworker arrives. Then do the less important things that you can manage to complete even if he's around, despite only having limited focus. Same reasoning to work later but then leave the high focus tasks till after he left ofcourse. I have a couple of coworkers that only arive at work at 11am. Be sure it's allowed though!
4) Talk with chatty coworker and try to get an agreement on at least a certain time window where he cannot have smalltalk at all. As long as you're at least open to some compromise it shouldn't be too much of an issue.
5) Kindly remind your chatty coworker that you're trying to focus. (you can't use this constantly, but it's pretty effective to get at least an hour or 2 a day of high-focus time). How to ask might vary depending on how often he's been distracting you and on how good terms you want to stay with him. Some options are:
- Would you mind keeping quiet for half an hour or so? I'm trying to get this tricky task done and need all the focus I can get, thanks.
- Could you take your puppy/children/party/... conversation to the watercooler/coffee machine/breakroom instead please?
- Some of us are at least trying to get some work done here ... do you mind *glare*?
The less friendly you use those, the more effective they are at getting some quiet time, at the cost of no longer getting invited to after office parties (best case) or not being able to ask him for help on small stuff (possibly worst case?). Depending on your job this is way more important to have than the quiet time though ... so be careful with how unkind you want to be :)
6) Go to a silent desk for an hour to get a tricky task done. See with your superior which quiet places are available for this. Perhaps you can even reserve a meeting room during certain hours (like early in the morning, last hour or 2 in the day) where you can sit alone.
7) See if you can change to another team that has people who prefer silence as well. If you're not the only one reminding a potential chatty person that silence is preferable they're much more likely listen.
8) Remind yourself that you're not expected to give 100% all day long, every day. Your company has decided that the advantages of open-office plan are more important than the disadvantages. That you're getting distracted now is part of their choice. Combine with the first option here so you get the feeling yourself that "you have done whatever you could, so now it's on them".