= Solution
The $3d$ and $4s$ <atomic orbitals> of <chromium> are close enough in energy that electron-electron terms can overturn the simple filling order. The configuration $[\mathrm{Ar}]\,3d^54s^1$ permits five singly occupied $3d$ orbitals and a parallel-spin $4s$ electron. Relative to $3d^44s^2$, it removes the $4s$ pair and permits more parallel-spin exchange interactions, lowering the Coulomb-and-exchange contribution enough to offset the orbital promotion cost.
As qualitative bookkeeping, six parallel <electron spins> give $\binom62=15$ same-spin pairs, compared with $\binom52=10$ in high-spin $3d^44s^2$. The individual <exchange integrals> are unequal, so this is an explanation of the tendency, rather than a quantitative atomic energy calculation. The observed <ground state> configuration is $\boxed{[\mathrm{Ar}]\,3d^54s^1}$.<Energy levels of neutral chromium in the NIST Handbook>[Cr I ground level, 3d5(6S)4s, a7S, J=3, energy 0 cm−1]{ref}
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