Chipless RFID sensor is currently one of the most promising sensor designs, especially in food safety sector, because it has a robust structure and is inexpensive for mass production. This paper proposes a simple, compact, and low-cost chipless RFID sensor tag for frozen food monitoring. The system consists of an interrogator antenna, which is an antipodal Vivaldi antenna, and a chipless RFID sensor tag inside a flat container that contains a small quantity of ice. When receiving power from the interrogator antenna, the sensor alters the frequency of the reflected signal if the ice melts. One of three states of the material in the container can be detected, i.e. ice, water, and air (empty container). The peak of the frequency response exhibits distinctively narrow 3-dB bandwidth of 35 -49 MHz, allowing multiple sensors to operate simultaneously within limited bandwidth and space; Peak center frequency is observed at 751 MHz or 838 MHz, for respectively ice and air, with no peak present for water. The system is simulated, analysed, and verified by measuring in free open space in a realistic environment. The measurement for ice melting over time is also measured and shown that frequencies of the peaks are slowly decreasing during the first 10 minutes after defrost and completely disappears after 15 minutes. The resonant peak reappears at 826 MHz after the tag is completely dry. A good tolerance to the background is also found when complex dielectric material is placed next to the sensor.