  The high-latitude Galactic H I cloud toward the extragalactic radio source 3C
225 is characterized by very narrow 21 cm emission and absorption indicative of
a very low H I spin temperature of about 20 K. Through high-resolution optical
spectroscopy, we report the detection of strong, very narrow Na I absorption
corresponding to this cloud toward a number of nearby stars. Assuming that the
turbulent H I and Na I motions are similar, we derive a cloud temperature of 20
(+6, -8) K (in complete agreement with the 21 cm results) and a line-of-sight
turbulent velocity of 0.37+/-0.08 km/s from a comparison of the H I and Na I
absorption linewidths. We also place a firm upper limit of 45 pc on the
distance of the cloud, which situates it well inside the Local Bubble in this
direction and makes it the nearest-known cold diffuse cloud discovered to date.
