It is sunnah to talk while eating. The Prophet (peace and blessings be upon him) is reported to have used to talk while eating. Here are some hadiths:
1- Jabir ibn `Abdillah (may Allah be pleased with him) reports that Allah’s Messenger (peace and blessings be upon him) asked his family for condiment. They (the members of his household) said: We have nothing with us but vinegar. He (the Prophet) asked for it, he began to eat it, and then said: “Vinegar is a good condiment, vinegar is a good condiment.” (Reported by Muslim)
2- `Umar ibn Abi Salamah narrates: I was a boy under the care of Allah’s Messenger and my hand used to go around the dish while I was eating. So Allah’s Messenger said to me: “O boy! Mention the Name of Allah and eat with your right hand, and eat of the dish that is nearer to you.” Since then I have followed those manners when eating. (Reported by Al-Bukhari and Muslim)
Based on the above-mentioned hadiths, we conclude that talking while eating is sunnah and not haram (unlawful). But, we should bear in mind that the chatting should be on something good and useful, since idle talk is not lawful, at all times, while having a meal or not.