Aspergillus is one of the most diverse genera, and it is chemically profound and known to produce many biologically active secondary metabolites. In the present study, a new aspochalasin H1 (1), together with nine known compounds (2–10), were isolated from a Hawaiian plant-associated endophytic fungus Aspergillus sp. FT1307. The structures were elucidated using nuclear magnetic resonance (NMR) (¹H, ¹H-¹H COSY, HSQC, HMBC, ROESY and 1D NOE), high-resolution electrospray ionization mass spectroscopy (HRESIMS), and comparisons with the reported literature. The absolute configuration of the new compound was established by electronic circular dichroism (ECD) in combination with NMR calculations. The new compound contains an epoxide moiety and an adjacent trans-diol, which has not been reported before in the aspochalasin family. The antibacterial screening of the isolated compounds was carried out against pathogenic bacteria (Staphylococcus aureus, Methicillin-resistant S. aureus and Bacillus subtilis). The antiproliferative activity of compounds 1–10 was evaluated against human breast cancer cell lines (MCF-7 and T46D) and ovarian cancer cell lines (A2780).