Shaykh Ibn Uthaymeen was asked:
I saw a man who was reciting the Quran and there was gum in his mouth. What is the ruling on that? If he ate leeks after the isha prayer and says that the time [between ‘Isha and Fajr] is long and I also use a toothbrush and toothpaste before the Fajr prayer. [However], the gum decreases the scent [of the leeks] and I eat it as [a form of] medicine because the doctors have said that gum cleans the stomach? So benefit us, may Allah reward you with good.
“First, I do not think he can establish the letters [of the Quran] if he recites and he is chewing gum. This is because the exiting points of the letters (مخارج ) will be preoccupied with chewing the gum. And it is well-known that it is not allowed for a person to recite the Quran, except if he makes the letters apparent [during the recitation of the Quran] to the best of his ability. If he wants to recite the Quran, then let him leave off the gum…”
[Liqaa Bab al-Maftooh no. 148]
Faisal Ibn Abdul Qaadir Ibn Hassan