  A detailed 3D distribution of interstellar matter in the solar neighborhood
is increasingly necessary. As part of a 3D mapping program, we aim at assigning
a precise distance to the high-latitude HI gas in particular the northern part
(b \geq 55^{circ}) of the shell associated with the conspicuous radio continuum
Loop I. This shell is thought to be the expanding boundary of an interstellar
bubble inflated and recently reheated by the strong stellar winds of the nearby
Scorpius-Centaurus OB. We recorded high-resolution spectra of 30 A-type target
stars located at various distances in the direction of the northern part of
Loop I. Interstellar NaI 5889-5895 and CaII K-H 3934-3968 {\AA} are modeled and
compared with the HI emission spectra from the LAB Survey. About two-thirds of
our stellar spectra possess narrow interstellar lines. Narrow lines are located
at the velocity of the main, low-velocity Loop 1 HI shell ([-6,+1] km/s in the
LSR). Using Hipparcos distances to the target stars, we show that the closest
boundary of the b geq+70^{\circ} part of this low-velocity Loop I arch is
located at of 98 \pm 6 pc. The corresponding interval for the lower-latitude
part (55^{\circ} \leq b \leq 70^{\circ}) is 95-157 pc. However, since the two
structures are apparently connected, the lower limit is more likely. At
variance with this shell, the second HI structure, which is characterized by
LSR Doppler velocities centered at -30 km/s, is NOT detected in any of the
optical spectra. It is located beyond 200 parsecs or totally depleted in NaI
and CaII. We discuss these results in the light of spherical expanding shells
and show that they are difficult to reconcile with simple geometries and a
nearby shell center close to the Plane. Instead, this high-latitude gas seems
to extend the inclined local chimney wall to high distances from the Plane.
