OtoHNS_MD is right, there are saliva glands that can swell if blocked, especially if there's a stone. If the stone's stuck an ENT can help get it out. Drinking lots of water helps.
Is there pain? One of the salivary glands is located under the chin on the sides or the neck. The gland could swell when eating if there is a blockage or narrowing of the duct. You could try drinking more water and taking lemon drops, or even lemon slices. If this doesn't work, see an Otolaryngologist, or your primary MD.