  We propose a method to suppress the chemical reactions between ultracold
bosonic ground-state $^{23}$Na$^{87}$Rb molecules based on optical shielding.
By applying a laser with a frequency blue-detuned from the transition between
the lowest rovibrational level of the electronic ground state $X^1\Sigma^+
(v_X=0, j_X=0)$, and the long-lived excited level $b^3\Pi_0 (v_b=0, j_b=1)$,
the long-range dipole-dipole interaction between the colliding molecules can be
engineered, leading to a dramatic suppression of reactive and photoinduced
inelastic collisions, for both linear and circular laser polarizations. We
demonstrate that the spontaneous emission from $b^3\Pi_0 (v_b=0, j_b=1)$ does
not deteriorate the shielding process. This opens the possibility for a strong
increase of the lifetime of cold molecule traps, and for an efficient
evaporative cooling. We also anticipate that the proposed mechanism is valid
for alkali-metal diatomics with sufficiently large dipole-dipole interactions.
