Using teeth whitening products in moderation should do no harm to your teeth as long as you do not leave the teeth whitening product on your teeth too long and do not over use the teeth whitening products.
However if you do use the teeth whitening products too often or use the teeth whitening products too often then yes they can cause your teeth to chip.
The chemicals used in teeth whitening and teeth whitening products can erode your teeth enamel and erode your teeth which leads to tooth decay and possible teeth chipping overtime.
It can take a few years to have your teeth become chipped after using the teeth whitening products but it has happened to me so I slowed down on the amount of teeth whitening products I use.
Use the teeth whitening products in moderation and your teeth should be white and healthy and not have any chips or cracks.