Maybe a start:
\documentclass{standalone}
\usepackage[LSB,LSBC3,T1]{fontenc}
\usepackage{chessboard}
\storechessboardstyle{8x8}{%
maxfield=h8,
borderwidth=10mm,
boardfontencoding=LSBC3,
color=white,
colorwhitebackfields,
color=black,
colorblackbackfields,
blackfieldmaskcolor=black,
whitepiececolor=yellow,
whitepiecemaskcolor=red,
addfontcolors,
pgfstyle=border,
color=white,
markregion=a1-h8,
}
\begin{document}
\chessboard[
style=8x8,
setwhite={Qa8,Qb4,Qc1,Qd3,Qe6,Qf2,Qg7,Qh5},
pgfstyle=straightmove,
arrow=stealth,
linewidth=.5ex,
padding=1ex,
color=blue!75!white,
pgfstyle=straightmove,
shortenstart=1ex,
showmover=true,
markmoves={d3-h7,d3-a6,d3-b1,d3-f1,d3-d8,d3-d1,d3-a3,d3-h3},
]
\end{document}

For straighter arrows:
\documentclass{standalone}
\usepackage[LSB,LSBC3,T1]{fontenc}
\usepackage{chessboard}
\usetikzlibrary{arrows.meta}
\makeatletter
\cbDefinePgfMoveStyle{mystraightmove}{%
\pgfsetlinewidth{\board@pgf@linewidth}%
\setlength\len@board@tempx{\dimexpr 0.1em + \board@pgf@shortenstart \relax}%
\pgfsetshortenstart{\len@board@tempx}%
\setlength\len@board@tempx{\board@pgf@shortenend}%
\pgfsetshortenend{\len@board@tempx}%
\pgfsetarrowsend{\board@pgf@arrow}%
\pgfsetrectcap
\pgfpathmoveto{\pgfpointorigin}%
\pgfpathlineto{\pgfpointanchor{#1}{center}}%
\pgfusepath{stroke}}%
\makeatother
\storechessboardstyle{8x8}{%
maxfield=h8,
borderwidth=10mm,
boardfontencoding=LSBC3,
color=white,
colorwhitebackfields,
color=black,
colorblackbackfields,
blackfieldmaskcolor=black,
whitepiececolor=yellow,
whitepiecemaskcolor=red,
addfontcolors,
pgfstyle=border,
color=white,
markregion=a1-h8,
}
\begin{document}
\chessboard[
style=8x8,
setwhite={Qa8,Qb4,Qc1,Qd3,Qe6,Qf2,Qg7,Qh5},
pgfstyle=mystraightmove,
linewidth=.5ex,
padding=1ex,
color=blue!75!white,
arrow={Triangle[width=1.5ex, length=1ex]},
shortenstart=1ex,
shortenend=-.5ex,
showmover=false,
markmoves={d3-h7,d3-a6,d3-b1,d3-f1,d3-d8,d3-d1,d3-a3,d3-h3},
]
\end{document}

I tried to figure out a way to wrap the arrows in a pgf transparency group so that I could make them partially transparent without weirdness. However, when I tried this, the arrows disappeared altogether and I couldn't figure it out.
xskakeinstead. It's more flexible – skpblack Sep 03 '14 at 21:32