When people eat with me for the first time, they can find themselves in a quandary. What to do when there is food in their mouths, but they want to say something immediately? They can't cover their lips, because otherwise I cannot understand them. Even if you're not likely to eat dinner with me in person, there's still a good chance that you'll end up at the table with a deaf person at some chance, and it's good to know ahead of time what the most problematic areas are, right?
Now, if you're really good at being a tidy chewer, and it's something containable and not all creamy, you might be able to get away with it (my family is actually really good, which is quite nice!). If in doubt, you can ask, "am I chewing discreetly enough or should I just finishing chewing first?" I certainly don't mind waiting - especially if you're eating sour cream. Please, please finish that sour cream and take a drink of something before talking. Watching a mouth full of sour cream move is disgusting. (Cream cheese and other sticky things are problematic as well, but sour cream is the worst).
Another thing that really helps is brushing your teeth before dinner (some dentists are now saying this is better for your enamel anyhow). Foods like beets, cherries and wine that normally stain your teeth will not adhere so well to freshly brushed teeth. Otherwise, even if you're done chewing, you could still be presenting your resident lipreader with a mouth full of purple teeth. Eeeeew. (Yes, this has happened to me. And hence the reason that I never serve beets or cherries).
Discreet chewing and tidy teeth will be appreciated everywhere, from business meetings to lunch with your grandmother, but probably nowhere more so than by a lipreader.