Is it permissible to speak while the Imam is delivering the Khutbah (sermon)?

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Speaking to the Khateeb (preacher) or to someone whom the Khateeb addresses is not prohibited. The evidence for this is the action of the Prophet, peace be upon him, who asked Sulayk al-Ghatafani, who had just entered while the Prophet was preaching, whether he had prayed. Furthermore, when a man entered during Umar ibn al-Khattab's Friday sermon, Umar questioned him regarding the time, and the man replied that he was occupied and only performed Wudu (ablution) after hearing the call. Umar then questioned the sufficiency of Wudu when the Prophet commanded Ghusl (ritual bath). The underlying reason for the prohibition of speech during the sermon is the distraction from the obligatory act of listening and hearing the sermon, which does not occur when speaking to the Khateeb or when addressing a necessary need.