'feeble chance' is correct and usable in written English.
You can use it to describe a small or slim chance of something occurring. For example, "He had a feeble chance of winning the competition, but he did it anyway."
And with rich-world economies still feeble, there is little chance that monetary conditions will suddenly tighten.
But the strong chance of feeble growth in the second quarter the National Institute of Economic and Social Research is forecasting a rise in GDP of only 0.3%—means that a cut in August is on the cards.
Without a union, even a feeble one, the mall workers don't stand a chance.
But if the German chancellor can force through his labour-market and welfare reforms without his habitual backsliding (see article), he has at least a chance of starting to recharge Germany's feeble economic batteries.
"I thought I'd return the favor and look down on her for a dream she has no chance of getting," he sighs in a feeble rationale for his own fecklessness.
But even a feeble power-play unit can score if given a lot of chances, and the Islanders gave Pittsburgh seven power plays.
If by chance they passed each other in the hallway, they would mumble feeble greetings and continue on their way.
Growth has been feeble, we've had a double dip recession and there is still the chance of a third.
Fortunately, there is no chance that laptops will revert to the days of hefty weight and feeble performance.
Aaron Boone, who is 4 for 33 as a Yankee, had a chance to give the Yankees a lead, but Rafael Soriano retired him on a feeble pop-up to first.
