We propose the deep progressive image compression using trit-planes (DPICT) algorithm, which is the first learning-based codec supporting fine granular scalability (FGS). First, we transform an image into a latent tensor using an analysis network. Then, we represent the latent tensor in ternary digits (trits) and encode it into a compressed bitstream trit-plane by trit-plane in the decreasing order of significance. Moreover, within each trit-plane, we sort the trits according to their rate-distortion priorities and transmit more important information first. Since the compression network is less optimized for the cases of using fewer tritplanes, we develop a postprocessing network for refining reconstructed images at low rates. Experimental results show that DPICT outperforms conventional progressive codecs significantly, while enabling FGS transmission. Codes are available at https://github.com/jaehanlee-mcl/DPICT.