I am friends with a stutterer, some help please?

I am friends with a stutterer, some help please? Last semester I met my friend through our bio lab, we were lab partners. We ended up becoming friends and studying for a variety of classes together. Come this semester we share some classes as well and have a set time once a week where we study for classes. And as I mentioned, he has a pretty severe stutter, its quite difficult to talk with him. He seems to really like me as a friend and the feeling is mutual. He sent me this long 'thank you' note at the end of last semester for the 'help' I gave him studying together (in all honesty he probably helped me more than I helped him, which I told him). So I ask, what should I know? What should I do? When he is trying to get a word across and really working on it and I know exactly which word he is looking for, do I chime in and say it? Or do I let him struggle until he gets it? I just feel so bad because he is such a nice and cool guy and I think this stuttering thing makes him awfully self-conscious. And when he is struggling for a word, and it is taking a long time, it just seems, almost painful for him. He is a great guy this friend of mine. I just want to know what I should do, and if there is anything else I should know. Thank you so much!