  We report 18 dust continuum detections ($\geq 3.3\sigma$) at $\sim88{\rm \mu
m}$ and $158{\rm \mu m}$ out of 49 ultraviolet(UV)-bright galaxies ($M_{\rm UV}
< -21.3$ mag) at $z>6.5$, observed by the Cycle-7 ALMA Large Program, REBELS
and its pilot programs. This has more than tripled the number of dust continuum
detections known at $z>6.5$. Out of these 18 detections, 12 are reported for
the first time as part of REBELS. In addition, 15 of the dust continuum
detected galaxies also show a [CII]$_{\rm 158{\rm \mu m}}$ emission line,
providing us with accurate redshifts. We anticipate more line emission
detections from six targets (including three continuum detected targets) where
observations are still ongoing. The dust continuum detected sources in our
sample tend to have a redder UV spectral slope than the ones without a dust
continuum detection. We estimate that all of the sources have an infrared (IR)
luminosity ($L_{\rm IR}$) in a range of $3-8 \times 10^{11} L_\odot$, except
for one with $L_{\rm IR} = 1.5^{+0.8}_{-0.5} \times 10^{12}\,L_{\odot}$. Their
fraction of obscured star formation is significant at $\gtrsim 50\%$. Some of
the dust continuum detected galaxies show spatial offsets ($\sim 0.5-1.5''$)
between the rest-UV and far-IR emission peaks. These separations appear to have
an increasing trend against an indicator that suggests spatially decoupled
phases of obscured and unobscured star formation. REBELS offers the best
available statistical constraints on obscured star formation in UV-bright,
massive galaxies at $z > 6.5$.
