  We prepare a chemically and thermally one-dimensional (1d) quantum degenerate
Bose gas in a single microtrap. We introduce a new interferometric method to
distinguish the quasicondensate fraction of the gas from the thermal cloud at
finite temperature. We reach temperatures down to $kT\approx
0.5\hbar\omega_\perp$ (transverse oscillator eigenfrequency $\omega_\perp$)
when collisional thermalization slows down as expected in 1d. At the lowest
temperatures the transverse momentum distribution exhibits a residual
dependence on the line density $n_{1d}$, characteristic for 1d systems. For
very low densities the approach to the transverse single particle ground state
is linear in $n_{1d}$.
