Silene latifolia is a dioecious plant with heteromorphic sex chromosomes that have originated only similar to 10 million years ago and is a promising model organism to study sex chromosome evolution in plants. Previous work suggests that S. latifolia XY chromosomes have gradually stopped recombining and the Y chromosome is undergoing degeneration as in animal sex chromosomes. However, this work has been limited by the paucity of sex-linked genes available. Here, we used 35 Gb of RNA-seq data from multiple males (XY) and females (XX) of an S. latifolia inbred line to detect sex-linked SNPs and identified more than 1,700 sex-linked contigs (with X-linked and Y-linked alleles). Analyses using known sex-linked and autosomal genes, together with simulations indicate that these newly identified sex-linked contigs are reliable. Using read numbers, we then estimated expression levels of X-linked and Y-linked alleles in males and found an overall trend of reduced expression of Y-linked alleles, consistent with a widespread ongoing degeneration of the S. latifolia Y chromosome. By comparing expression intensities of X-linked alleles in males and females, we found that X-linked allele expression increases as Y-linked allele expression decreases in males, which makes expression of sex-linked contigs similar in both sexes. This phenomenon is known as dosage compensation and has so far only been observed in evolutionary old animal sex chromosome systems. Our results suggest that dosage compensation has evolved in plants and that it can quickly evolve de novo after the origin of sex chromosomes.