Q) I found chometz in my house on Pesach. What should I do?
A) The Shulchan Aruch (OC 446:1) tells us that one who finds chometz (that he owns) in his house on Chol Hamo’ed Pesach should take it out of his house and destroy it immediately.
If the chometz was found on Yom Tov itself; he should cover it and destroy it at the conclusion of Yom Tov [i.e. on chol hamo’ed].
The Remo (ibid) explains that the chometz cannot be moved on Yom Tov and taken out of his domain because it is muktzeh, and also one cannot burn chometz on Yom Tov.
The Mishna Berura (s.k. 6) brings differing opinions about chometz that has not been nullified – the example the Mishna Berura discusses is a dough that became chometz on Pesach, and was therefore not included in the kol chamira declaration before Pesach. [Ostensibly, another situation could be if the person did not say kol chamira before Pesach.]
In such a circumstance, where the chometz has not been nullified and the person who owns it is now transgressing the prohibition of bal yero’eh, some authorities rule that the issur d’orayso of bal yero’eh overrides the rabbinic prohibition of muktzeh and therefore one can, and should, move the chometz and destroy it in a way that is permissible on Yom Tov – e.g. by disposing of it in a river or in a toilet. Some even allow one to burn the chometz on Yom Tov.
Nevertheless, the conclusion of the Mishna Berura is that in all situations one should only cover the chometz on Yom Tov, and destroy it as soon as is possible on Motzo’ei Yom Tov.