Aside from polyploidy, transposable elements are the major drivers of genome size increases in plants. Thus, understanding the diversity and evolutionary dynamics of transposable elements in sunflower (Helianthus annuus L.), especially given its large genome size (∼3.5 Gb) and the well‐documented cases of amplification of certain transposons within the genus, is of considerable importance for understanding the evolutionary history of this emerging model species. By analyzing approximately 25% of the sunflower genome from random sequence reads and assembled bacterial artificial chromosome (BAC) clones, we show that it is composed of over 81% transposable elements, 77% of which are long terminal repeat (LTR) retrotransposons. Moreover, the LTR retrotransposon fraction in BAC clones harboring genes is disproportionately composed of chromodomain‐containing Gypsy LTR retrotransposons (‘chromoviruses’), and the majority of the intact chromoviruses contain tandem chromodomain duplications. We show that there is a bias in the efficacy of homologous recombination in removing LTR retrotransposon DNA, thereby providing insight into the mechanisms associated with transposable element (TE) composition in the sunflower genome. We also show that the vast majority of observed LTR retrotransposon insertions have likely occurred since the origin of this species, providing further evidence that biased LTR retrotransposon activity has played a major role in shaping the chromatin and DNA landscape of the sunflower genome. Although our findings on LTR retrotransposon age and structure could be influenced by the selection of the BAC clones analyzed, a global analysis of random sequence reads indicates that the evolutionary patterns described herein apply to the sunflower genome as a whole.