Is it permissible to recite Qur'an while performing household chores (in kitchen, for example), or does getting the reward for reciting Qur'an requires that one should be doing nothing else while reciting?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

'Aa'ishah said: "The Prophet used to mention Allaah at all times." The author of Tuhfatul-Ahwathi said (while explaining this Hadeeth): "At all times means in all conditions whether or not he is in the state of purity, while walking, sitting, standing and lying down." Reciting the Quran is among the mention of Allaah; rather, it is the highest type of the mention of Allaah. However, the Hadeeth does not include some situations, such as while a person is answering his call of nature or having sex with his wife, etc.  Also when a person is in the state of major ritual impurity, he should not recite the Quran for the Hadeeth of the Prophet narrated by 'Ali who said: "He (the Prophet ) used to teach us the Quran in all conditions except when he is in the state of sexual impurity."

Therefore, one may recite the Quran during the household work or any other work and the person will get the reward of reciting the Quran for the general meaning of the Hadeeth: "Whenever a person recites a letter from the Book of Allaah one good deed is recorded for him."  [At-Tirmithi]

However, the grades of reward may vary from one person to another based on his degree of submissiveness and reflection while reciting.

Allaah Knows best.