We provide X-ray constraints and perform the first X-ray spectral analyses for bright SCUBA sources ( f 850µm ≥ 5 mJy; S/N≥ 4) in an 8. ′ 4 × 8. ′ 4 area of the 2 Ms Chandra Deep Field-North survey containing the Hubble Deep Field-North. X-ray emission is detected from seven of the ten bright submm sources in this region down to 0.5-8.0 keV fluxes of ≈ 1 × 10 −16 erg cm −2 s −1 , corresponding to an X-ray detected submm source density of 360 +190 −130 deg −2 ; our analyses suggest that this equates to an X-ray detected fraction of the bright submm source population of > ∼ 36%, although systematic effects may be present. Two of the X-ray detected sources have nearby (within 3 ′′ ) X-ray companions, suggesting merging/interacting sources or gravitational lensing effects, and three of the X-ray detected sources lie within the approximate extent of the proto-cluster candidate CXOHDFN J123620.0+621554. Five of the X-ray detected sources have flat effective X-ray spectral slopes (Γ < 1.0), suggesting obscured AGN activity. X-ray spectral analyses suggest that one of these AGNs may be a Compton-thick source; of the other four AGNs, three appear to be Compton-thin sources and one has poor constraints. The rest-frame unabsorbed X-ray luminosities of these AGNs are more consistent with those of Seyfert galaxies than QSOs (i.e., L X ≈ 10 43 -10 44 erg s −1 ). Thus, the low X-ray detection rate of bright submm sources by moderately deep X-ray surveys appears to be due to the relatively low luminosities of the AGNs in these sources rather than Compton-thick absorption. A comparison of these sources to the well-studied heavily obscured AGN NGC 6240 shows that the average AGN contribution is negligible at submm wavelengths. The X-ray properties of the other two X-ray detected sources are consistent with those expected from luminous star formation; however, we cannot rule out the possibility that low-luminosity AGNs are present. The three X-ray undetected sources appear to lie at high redshift (z > 4) and could be either AGNs or starbust galaxies.