  We investigate tensionless (or null) bosonic string theory with a Kalb-Ramond
background turned on. In analogy with the tensile case, we find that the
Kalb-Ramond field has a non-trivial effect on the spectrum only when the theory
is compactified on an (\left(S^1\right)^{\otimes d}) background with (d\geq 2).
We discuss the effect of this background field on the tensionless spectrum
constructed on three known consistent null string vacua. We elucidate further
on the intriguing fate of duality symmetries in these classes of string
theories when the background field is turned on.
