The defender, who has been a regular in the Tigers' backline this season, suffered a hamstring tear against Aston Villa and is now in a race to be fit to face Arsenal
The Tigers meet Arsenal at Wembley on May 17 in their first ever FA Cup final but have a number of players currently sidelined, with Chester the latest to pick up an injury in a 3-1 defeat at Aston Villa at the weekend.
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"The scan has confirmed that James has a tear in the hamstring, although it’s not as bad as the last two times," he told reporters
"He’s got 10 days and we’ll give him every chance."
There is better news, however, for fellow defender Paul McShane (ankle) and goalkeeper Allan McGregor (kidney).
"Paul came through another hour of football (in a behind-closed-doors friendly on Tuesday) and we'll take a look at him to see if he's available for the weekend (against Everton)," added Bruce.
"Allan is on course and he trained on Tuesday. We’ll see how he is over the next couple of days and he’s got a chance."