  We have measured our Galaxy's motion relative to distant galaxies in which
type Ia supernovae (SN Ia) have been observed. The effective recession velocity
of this sample is 7000 km s$^{-1}$, which approaches the depth of the survey of
brightest cluster galaxies by Lauer and Postman (1994). We use the Light Curve
Shape (LCS) method for deriving distances to SN Ia, providing relative distance
estimates to individual supernovae with a precision of $\sim$ 5\% (Riess,
Press, \& Kirshner 1995). Analyzing the distribution on the sky of velocity
residuals from a pure Hubble flow for 13 recent SN Ia drawn primarily from the
Cal\'{a}n/Tololo survey (Hamuy 1993a, 1994, 1995a, 1995b, Maza et al. 1994), we
find the best solution for the motion of the Local Group in this frame is 600
$\pm 350$ km s$^{-1}$ in the direction b=260$\deg$ {\it l}=+54$\deg$ with a 1
$\sigma$ error ellipse that measures 90$\deg$ by 25$\deg$. This solution is
consistent with the rest frame of the cosmic microwave background (CMB) as
determined by the Cosmic Background Explorer (COBE) measurement of the dipole
temperature anisotropy (Smoot et al. 1992). It is inconsistent with the
velocity observed by Lauer and Postman.
