Ternary logic has been investigated for several years as it can provide substantial advantages in reducing the complexity of operations and the number of interconnects. On the other hand, with the advancement of technology and the reduction of the feature size and supply voltage, the sensitivity of memory elements to radiation effects has increased. In this paper, a robust ternary SRAM (TSRAM) cell is designed using a novel ternary C-element based on carbon nanotube field-effect transistors (CNTFETs). Besides, a 2m×2n ternary memory array architecture is designed and simulated based on the proposed TSRAM cell. Unlike the previous TSRAM cells, our proposed cell is hardened against radiation effects caused by high-energy particle strikes, which is a significant achievement in ternary memory design. Our extensive simulations demonstrate that the proposed radiation-hardened TSRAM offers up to 77× higher critical charge and up to 98 % higher SNM at the cost of 47 % to 65 % area overhead. It is also noteworthy that the proposed design only needs only two threshold voltages. Moreover, the proposed TSRAM is robust against the process and temperature variations. Our results emphasize that the proposed design is a milestone for designing high-performance, radiation-hardened, and robust ternary memory chips.