Can I cut up chicken and store it in the fridge until the use-by date?
In general, assuming that the date on the package still applies after the package has been opened is not safe.

If an item is packaged under special conditions (sterile, low oxygen, the strange diaper thing, etc.), or treated after packaging (irradiated, pasteurized, etc.) then the time from when you break the seal on the package becomes more significant than the 'best by' date on the package.

As a comparison, we have bottled liquids like juice or various 'milk' (plant milks or UHT treated cow's milk) -- they might have a 'best by date' that's many months from packaging, but they'll often have a warning to use it within a given number of days from opening it.

If you buy cryovaced packages of meat, it will have some sort of a date (eg. 'sell by' or 'use or freeze by') on it that might be up to a month from when it was packaged ... but once you open the package, you should treat it like any other raw meat that hasn't been specially packaged.

Now, is there a bit of a safety factor built into the normal 1-2 day advice?  I would hope so ... to deal with the time that you're walking round the store with the chicken in your basket, time to get it home, etc.  So it's possible that it might be a little longer than the 1-2 days, so 2-4 days is likely acceptable provided that you've held at the proper temperature, you cook it thoroughly and it wasn't showing other problems signs (smells, slime, etc.) and you're not cooking for immune compromised people.

Much past that, and you're just compounding your risk.  Now, there might be extenuating circumstances (eg, you're trapped at home with no way to resupply because of mass quarantines) on why you'd be willing to take the risk, but in general, I wouldn't recommend consuming the chicken from a package that was opened a week ago, even if it was within the date on the original package.