Yes, it will be fine for previously-refrigerated chicken.
The general rule is that any food (that normally needs refrigeration) must be kept out of the "danger zone" of certain temperatures longer than 4 hours.
(That 4 hrs includes ALL of the time though since slaughter, including once you take it out of the refrigerated case at the store and transport it home, and sometimes you won't know how well it's been stored by other people during all of that time.)
The danger zone is considered to be between 40º F (the normal temp in a well-functioning refrigerator) and 140º F (the temp of fish cooked to a safe temp).
So one hour outside that danger zone won't be a problem at all (unless the food had been very badly stored before that). And even then, if you cook the very-interior of that food to the proper "safe" temp, you'd kill off things like e.coli and salmonella.
Also, salt/sodium, sugars, and acids are natural preservatives, and you likely have some of those in your marinade which would be even better.