We observed with Chandra two peculiar galactic X-ray sources, 4U 1700+24 and 4U 1954+319, which are suspected to have a M-type giant star as optical counterpart, in order to get a high-precision astrometric position for both of them. The peculiarity of these sources lies in the fact that these are the only two cases among low-mass X-ray binaries (LMXBs), besides the confirmed case of GX 1+4, for which the companion can possibly be a M-type giant. We found that in both cases the field M-type giant star is indeed the counterpart of these X-ray sources. We also determined the distance to 4U 1954+319 to be ∼1.7 kpc. This result suggests that a number of faint (L X ∼ 10 32 −10 34 erg s −1 ) Galactic X-ray sources are "symbiotic X-ray binaries", that is, wide-orbit LMXBs composed of a compact object, most likely a neutron star, accreting from the wind of a M-type giant.