It shouldn't take a huge amount of force, assuming that the clip link mounting is the right size for the chain. Assuming it's an O-ring chain make sure you are not trying to jam the rollers through the push-on o-rings that come with the package. When I did Sophie's chain I used a pair of square ended pliers to squeeze the link through so that the two grooves were visible, then the same pliers to snap the retainer in to place.
Remember to put the closed end of the clip to the direction of travel of the chain! On the top run of the chain it will face closed end forward; on the bottom towards the back.
