Single-cell C4 (SCC4) plants with bienertioid anatomy carry out photosynthesis in a single cell. Chloroplast movement is the underlying phenomenon, where chloroplast unusual positioning 1 (CHUP1) plays a key role. This study aimed to characterize CHUP1 and CHUP1-like proteins in an SCC4 photosynthetic plant, Bienertia sinuspersici. Also, a comparative analysis of SCC4 CHUP1 was made with C3, C4, and CAM model plants including an extant basal angiosperm, Amborella. The CHUP1 gene exists as a single copy from the basal angiosperms to SCC4 plants. Our analysis identified that Chenopodium quinoa, a recently duplicated allotetraploid, has two copies of CHUP1. In addition, the numbers of CHUP1-like and its associated proteins such as CHUP1-like_a, CHUP1-like_b, HPR, TPR, and ABP varied between the species. Hidden Markov Model analysis showed that the gene size of CHUP1-like_a and CHUP1-like_b of SCC4 species, Bienertia, and Suaeda were enlarged than other plants. Also, we identified that CHUP1-like_a and CHUP1-like_b are absent in Arabidopsis and Amborella, respectively. Motif analysis identified several conserved and variable motifs based on the orders (monocot and dicot) as well as photosynthetic pathways. For instance, CAM plants such as pineapple and cactus shared certain motifs of CHUP1-like_a irrespective of their distant phylogenetic relationship. The free ratio model showed that CHUP1 maintained purifying selection, whereas CHUP1-like_a and CHUP1-like_b have adaptive functions between SCC4 plants and quinoa. Similarly, rice and maize branches displayed functional diversification on CHUP1-like_b. Relative gene expression data showed that during the subcellular compartmentalization process of Bienertia, CHUP1 and actin-binding proteins (ABP) genes showed a similar pattern of expression. Altogether, the results of this study provide insight into the evolutionary and functional details of CHUP1 and its associated proteins in the development of the SCC4 system in comparison with other C3, C4, and CAM model plants.