You might well continue to have a problem with distractions even if every person in the church did not say a word. Even the very silence might distract you. That's because distractions are common to prayer, no matter the condition in which you find yourself when trying to pray.
That doesn't mean you cannot try to cut down on distractions. If the parish refuses to address the problem with chatter in the sanctuary, then perhaps there is some way you might block the noise for yourself. Perhaps you might wear earplugs, if you can do so discreetly and without cutting yourself off from sounds you need to hear. I don't recommend making a big show of putting in your earplugs or wearing earmuffs that would be noticeable to those around you. It's one thing to cut down on distraction insofar as you can; it is quite another to make a spectacle of yourself at the expense of other people's feelings.