Tropical filamentous marine cyanobacteria have emerged as a viable source of novel bioactive natural products for drug discovery and development. In the present study, aplysiatoxin (1), debromoaplysiatoxin (2) and anhydrodebromoaplysiatoxin (3), as well as two new analogues, 3-methoxyaplysiatoxin (4) and 3-methoxydebromoaplysiatoxin (5), are reported for the first time from the marine cyanobacterium Trichodesmium erythraeum. The identification of the bloom-forming cyanobacterial strain was confirmed based on phylogenetic analysis of its 16S rRNA sequences. Structural determination of the new analogues was achieved by extensive NMR spectroscopic analysis and comparison with NMR spectral data of known compounds. In addition, the antiviral activities of these marine toxins were assessed using Chikungunya virus (CHIKV)-infected cells. Post-treatment experiments using the debrominated analogues, namely compounds 2, 3 and 5, displayed dose-dependent inhibition of CHIKV when tested at concentrations ranging from 0.1 µM to 10.0 µM. Furthermore, debromoaplysiatoxin (2) and 3-methoxydebromoaplysiatoxin (5) exhibited significant anti-CHIKV activities with EC50 values of 1.3 μM and 2.7 μM, respectively, and selectivity indices of 10.9 and 9.2, respectively.