The distance of the Pegasus Dwarf Irregular Galaxy is discussed in the light of new, deep photometry of the resolved stars taken in the bands V, R, and I of the Johnson-Cousins system. The tip of the red giant branch is identified beyond doubt. From its position, a distance modulus of (m - M)0 = 24.9 +/- 0.1 is derived, in disagreement with the previous estimate by Hoessel et al., based on Cepheid light curves (m - M)0 = 26.22 +/- 0.2). The new estimate of (m - M)0 = 24.9 implies that Pegasus is at about 0.64 Mpc from the center of gravity of the Local Group. This distance makes Pegasus a highly probable member of the Local Group and is consistent with the heliocentric velocity of this galaxy. Finally, a list of six Cepheid candidates is given on the basis of the new photometry.