Can someone get cancer from chemotherapy?

Yes but its rare: Chemicals of various kinds can be carcinogenic. Similarly chemotherapy drugs have a known small risk to cause secondary cancers. Two classes of Anticancer drugs are more prone to cause Cancer. These include alkylating agents(like Melphalan) and anthracyclines like Doxorubicin. The benefits of chemotherapy are much greater than the small risk(1-2% or lower) of causing cancer.