  The simplest possible noncommutative harmonic oscillator in two dimensions is
used to quantize the free closed bosonic string in two flat dimensions. The
partition function is not deformed by the introduction of noncommutativity, if
we rescale the time and change the compactification radius appropriately. The
four point function is deformed, preserving, nevertheless, the sl(2,C)
invariance. Finally the first Ward identity of the deformed theory is derived.
