That appears to be bolting. Even if the taller stalks are cut off they will still continue to get older. Chickory is sometimes bitter, but I think its the older leaves that tend to be that way.

So I should cut the stalks and it'll continue to grow from ground level? Okay, I can do that!

Bolting usually means that the p[lant gets taller and starts to go into flower and seed production mode. As mentioned in the past, there is not much you can do once a plant starts to bolt as it will not go back again. Cutting it back will not do anything but keep it smaller.

If your chicory is bolting, don't cut it. As others have already said, you can not stop it at this point. Best to enjoy what the bolting will bring - beautiful blue flowers and then the gold finches and other seed eating birds. Chicory is almost as popular as salsify and sunflowers in my garden with the seed eaters.

FataMorgana

Here is a link that might be useful: Chicory blooms

Gold Finches here love thistle seeds..