The known host galaxies of short-hard gamma-ray bursts (GRBs) to date are characterized by low to moderate star formation rates (SFRs) and a broad range of stellar masses, in general agreement with models associating the phenomenon with an old progenitor, such as merging neutron stars. In this paper, we positionally associate the recent unambiguously short-hard Swift GRB 100206A with a disk galaxy at redshift z = 0.4068 that is rapidly forming stars at a rate of åisebox-0.5ex 30 M $_☉$ yr$^-1$, almost an order of magnitude higher than any previously identified short-GRB host. The galaxy is very red (g - K = 4.3 AB mag), heavily obscured (A$_V$ ≈ 2 mag), and has the highest metallicity of any GRB host to date (12 + log[O/H]$_KD02$ = 9.2): it is a classical luminous infrared galaxy (LIRG), with L $_IR$ ≈ 4 × 10$^11$ L $_☉$. While these properties could be interpreted to support an association of this GRB with recent star formation, modeling of the broadband spectral energy distribution also indicates that a substantial stellar mass of mostly older stars is also present. The specific SFR is modest (sSFR ≈ 0.5 Gyr$^-1$), the current SFR is not substantially elevated above its long-term average, and the host morphology shows no sign of recent merger activity. Our observations are therefore equally consistent with an older progenitor. Given the precedent established by previous short-GRB hosts and the significant fraction of the universe's stellar mass in LIRG-like systems at z >i̊sebox-0.5ex 0.3, an older progenitor represents the most likely origin of this event.