A chemical study of the Vietnamese plant species Trigonostemon howii led to the isolation of a new tigliane-type diterpenoid, trigowiin A (1), along with several known coumarins and phenylpropanoids. The planar structure and the relative configuration of compound 1 were elucidated based on spectroscopic analysis, including 1D- and 2D-NMR experiments, mass spectrometry, and comparison with literature data. Trigowiin A (1) exhibited moderate antiviral activity in a virus-cell-based assay for Chikungunya virus (CHIKV). Since the structure of compound 1 is closely related to those of well-known tigliane diterpenoids such as prostratin (2), phorbol (3), 12-O-tetradecanoylphorbol 13-acetate (TPA) (4), and 4α-TPA (5), the antiviral activity of the latter compounds was also evaluated against CHIKV, as well as in virus-cell-based assays of two additional members of the genus Alphavirus (Sindbis virus, SINV, and Semliki forest virus, SFV). Whereas prostratin inhibited CHIKV replication with a moderate EC50 of 2.6 μM and a selectivity index (SI) approximating 30, compound 4 proved to be an extremely potent inhibitor, with an EC50 of 3 nM and a SI near 2000. Interestingly, no or very little activity was observed on the replication of SINV and SFV.