Mishna: On Pesach Sheini one may have Chometz . The implication of the Mishna’s language would seem to be that while one is eating the Pesach one may not also eat Chometz.
There is no explicit source for this Halacha, prior to Rashi on Chumash (Bamidbar 9:10), who does seem to clearly state that one may not eat Chametz together with the Pesach. The Acharonim discuss what the Torah source for this Halacha could be. One of the more interesting Pshatim is that of the Rogatchover (brought down קובץ כרם שלמה (שנה ז קו’ ז עמ’ י”ז) נדפס מכתב מהג”ר ראובן סגל זעהמאן זצ”ל (אב”ד אטווצק) , who declares that eating a Pesach is like burning a sacrifice on which the Torah says כי כל שאור וכל דבש לא תקטירו ממנו אשה לה’!.