We present millimeter- and submillimeter-wavelength observations and near-infrared K-band imaging toward the bright gamma-ray burst GRB 010222. Over seven different epochs, a constant source was detected with an average flux density of 3.74+/-0.53 mJy at 350 GHz and 1.05+/-0.22 mJy at 250 GHz, giving a spectral index α=3.78+/-0.25 (where Fåisebox-0.5extext asciitildeν$^α$). We rule out the possibility that this emission originated from the burst or its afterglow, and we conclude that it is due to a dusty, high-redshift starburst galaxy (SMM J14522+4301). We argue that the host galaxy of GRB 010222 is the most plausible counterpart of SMM J14522+4301, based in part on the centimeter detection of the host at the expected level. The optical/near-IR properties of the host galaxy of GRB 010222 suggest that it is a blue sub-L$_*$ galaxy, similar to other GRB host galaxies. This contrasts with the enormous far-infrared luminosity of this galaxy based on our submillimeter detection (L$_Bol$i̊sebox -0.5ex 4×10$^12$L$_solar$). We suggest that this GRB host galaxy has a very high star formation rate, SFR rs̊ebox-0.5ex 600 M$_solar$ yr$^-1$, most of which is unseen at optical wavelengths.