A major impediment to the response of tumors to chemotherapy is that the large majority of cancer cells within a tumor are quiescent in G0/G1, where cancer cells are resistant to chemotherapy. To attempt to solve this problem of quiescent cells in a tumor, cancer cells were treated with recombinant methioninase (rMETase), which selectively traps cancer cells in S/G2. The cell cycle phase of the cancer cells was visualized with the fluorescence ubiquitination-based cell cycle indicator cell cycle indicator (FUCCI). At the time of rMETase-induced S/G2-phase blockage, identified by the cancer cells' green fluorescence by FUCCI imaging, the cancer cells were administered S/G2-dependent chemotherapy drugs, which interact with DNA or block DNA synthesis such as doxorubicin, cisplatin, or 5-fluorouracil. Treatment of cancer cells with drugs only, without rMETase-induced S/G2 phase blockage, led to the majority of the cancer-cell population being blocked in G0/G1 phase, identified by the cancer cells becoming red fluorescent in the FUCCI system. The G0/G1 blocked cells were resistant to the chemotherapy. In contrast, trapping of cancer cells in S/G2 phase by rMETase treatment followed by FUCCI-imaging-guided chemotherapy was highly effective in killing the cancer cells.