  The exclusive radiative $B \to K^* \gamma$, $B \to K^*_2 \gamma$, $B_s \to
\phi \gamma$ and $\Lambda_b \to \Lambda \gamma$ decays are studied in a new
physics scenario with two universal extra dimensions compactified on a chiral
square. The computed branching fractions depend on the size $R$ of the extra
dimensions, and a comparison with the available measurements allows us to put
bounds on such a fundamental parameter. From the mode $B^0 \to K^{*0} \gamma$
we obtain the most stringent bound: $1 \over R>710$ GeV.
