In this paper, we study the fundamental limits of de novo transcriptome assembly using RNA shotgun-sequencing, where short reads are obtained from the RNA transcripts. We propose a new linear-time algorithm for transcriptome assembly and derive sufficient conditions on the length of reads under which the algorithm will succeed. We then compare them with necessary conditions that we derive for reconstruction by any algorithm, and show that the proposed algorithm is near-optimal on a real data set. We also describe the construction of a software package for RNA assembly based on this theory and show that it obtains significant improvements in reconstruction accuracy over state-of-the-art software.