On the basis of a new classification-resolution spectrum, we find that HR 8799, a known member of the newly discovered gamma Doradus variable star class, is a lambda Bootis star. Spectral synthesis, in conjunction with fluxes from visible spectrophotometry and the TD-1 satellite, yields T-eff = 7430 K, log g = 4.35, microturbulent velocity xi(t) = 2.7 km s(-1), and metallicity [M/H] = -0.47 for HR 8799, confirming its metal-weak nature. HR 8799 is also a "Vega-like" star in that it shows excess flux at 60 mu m, probably due to a circumstellar dust shell or disk. Thus, this star links three astrophysically interesting classes of stars and may provide potentially important constraints on the physics of, and the interconnections between, the lambda Bootis phenomenon and the gamma Doradus pulsation phenomenon.