私は毎日ガムを1パック(or 1袋)全部食べます。 in hiragana: わたし は まいにち がむ を ひとぱっく (or ひとふくろ) ぜんぶ たべます。 *We don't put any spaces between the Japanese words. *to chew means かむ and you can use it for this translation but たべる sounds more natural, at least yo me. I hope this was helpful.

「毎日ガムをかんでいます」が自然な表現だと思います。