The short answer is "No, it's likely that the store has no liability for the theft of your bike."
I am not a lawyer, so this longer answer is to the best of my layman's understanding
The key legal issue in the US is one of Bailment. For a bailment to be created the property in question has to be delivered to the bailee (the store or it's representative) by you (the bailor), and the bailee must have both possession and control of the property. Once a bailment has been created the bailee must take reasonable steps to care for the property that has been delivered but does not normally insure the bailor against all loss of or to the property while it is in the bailee's possession unless he expressly undertakes that obligation.
What this means is that the bailee is not liable for any and all damages or loss of the property while the property is in his care; he is only liable if the bailee can be proved negligent in caring for the property. Negligence can be proved if you can show that a reasonable person in possession and control of your property would not have taken whatever action led to the loss.
So, you rode up to a rack, chained up your bike and went your way. There was no transfer of possession or control from you to the store. The store couldn't move your bike (at least not under normal situations) and no individual implied in any way that they would look after or protect it. Even if it was obvious to a reasonable individual that the rack was poorly installed or easily circumvented, the bailment was not created in the first place, so the store has no duty whatsoever to protect your bike from theft or loss.
An overwhelming majority of cases covering automobiles have found no liability to the parking provider in similar cases. For example, when a customer pays a fee, drives his car to an available space, locks the car and takes the key, most US courts have held that you have merely leased space and that even with payment the control and possession of the vehicle necessary to constitute a bailment has not passed to the lot owner or operator.
If however you valet park your car, giving someone your keys in exchange for a claim ticket and they then park your car, which is subsequently stolen, you would likely have a claim because the operator/owner had not just possession but also control of the vehicle.
If you had been at some kind of event that had valet bike parking, then the answer might be different.
Here is a link about bailment with more information if you are part of the small segment of the population that has to know all the details (like me).