What is the electronic configuration of Cr (+1) ion
I assume we are talking about the free ions in the gas phase.

I checked my notes and it seems that the electronic configuration of $\ce{Cr+}$ should be $[\ce{Ar}]\mathrm{3d^5}$, the reference being a rather old book: Phillips &amp; Williams' Inorganic Chemistry (1966). I tried to look in slightly newer textbooks, but I couldn't find any information on the monovalent ions.

I would not claim to be 100% certain on this, but it can certainly be rationalised by the increase in $Z_\mathrm{eff}$ in the $\ce{Cr+}$ ion as compared to neutral $\ce{Cr}$ (one less electron means less shielding and greater effective nuclear charge). That would serve to stabilise the 3d orbital more than it stabilises the 4s orbital, and therefore favour the $\mathrm{3d^5}$ configuration over the $\mathrm{3d^44s^1}$ configuration.

In general, the electronic configurations of transition metals and their ions are a balance of delicate factors. It's not easy to rationalise the electronic configurations fully and there are several factors that will affect the configuration adopted, e.g. 1) nuclear charge and relative energy of 3d and 4s orbitals, 2) relative e-e repulsions in 3d and 4s orbitals, 3) exchange energy.

Some interesting discussion on the topic can be found here:  


J. Chem. Educ., 1978, 55(1), 2
J. Chem. Educ., 1989, 66(6), 481
J. Chem. Educ., 1994, 71(6), 469