  We report a single-crystal study on the magnetism of the rare-earth compound
PrTiNbO$_6$ that experimentally realizes the zigzag pseudospin-$\frac{1}{2}$
quantum antiferromagnetic chain model. Random crystal electric field caused by
the site mixing between non-magnetic Ti$^{4+}$ and Nb$^{5+}$, results in the
non-Kramers ground state quasi-doublet of Pr$^{3+}$ with the effective
pseudospin-$\frac{1}{2}$ Ising moment. Despite the antiferromagnetic intersite
coupling of about 4 K, no magnetic freezing is detected down to 0.1 K, whilst
the system approaches its ground state with almost zero residual spin entropy.
At low temperatures, a sizable gap of about 1 K is observed in zero field. We
ascribe this gap to off-diagonal anisotropy terms in the pseudospin
Hamiltonian, and argue that rare-earth oxides open an interesting venue for
studying magnetism of quantum spin chains.
