On Pesach, it is forbidden not only to eat Hametz and to have Hametz in one’s possession, but also to derive benefit from Hametz. This means that even if Hametz is owned by somebody else, one may not derive benefit from it.
Relevant to this Halacha, the Mishna Berura (450:23) addresses the situation of a gentile whose animal on Pesach crouches under the weight of its cargo, and the gentile needs help to unload some of the cargo, which consists of Hametz, in order to alleviate the animal’s burden. In principle, it should be forbidden for a Jew to assist the gentile, because he anticipates to receive something in return – either a tip, some reciprocation, or at least the gentile’s goodwill and friendship – and thus in effect, the Jew would be benefiting from the Hametz. Such a case would, seemingly, qualify as one of "Roseh Be’kiyumo" – where the Jew has vested interested in the Hametz’s existence on Pesach, which constitutes a form of forbidden benefit. However, the Mishna Berura rules that the Jew would be allowed to help the gentile unload the cargo, because the Jew’s intent is to avoid "Sa’ar Ba’aleh Hayim" – the pain suffered by the animal. The primary motivation for unloading the cargo is the Misva of alleviating the animal’s suffering, and he does not seek to derive any form of personal benefit. The Misva of preventing "Sa’ar Ba’aleh Hayim" does not Halachically constitute "Hana’a" ("benefit"), and so he may help the gentile in this case.
The Mishna Berura’s discussion likely becomes relevant in other similar situations that do not involve a Misva. A contemporary example would be a Jewish trucking company which is hired to transport food for a company owned by the gentiles, and the food is Hametz. The Jew clearly has vested interest in the existence of this Hametz, as it is the cause of a profitable contract. In light of the Mishna Berura’s discussion of the case involving an animal, it would appear that a Jewish truck driver or truck company should not transport a gentile’s Hametz on Pesach, as this would constitute "benefit" from Hametz which is forbidden on Pesach.
Summary: It is forbidden on Pesach not only to eat or own Hametz, but also to derive any form of benefit from somebody else’s Hametz, which includes putting oneself in a situation whereby the existence of Hametz is somehow beneficial. It would thus seem that a Jewish trucker should not transport a gentile’s Hametz during Pesach.
