Hill-Wood, 76, was taken ill on Friday following a bout of pneumonia.
“Everyone at Arsenal Football Club sends their support and best wishes to chairman Peter Hill-Wood. Peter is making a good recovery,” said a club statement.
“The club wishes Peter a full and speedy return to health and our thoughts are with him and his family at this time.”
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.