This line was said by Sheldon Cooper in the Big Bang Theory. I have looked up the meaning of the word "tier" in many dictionaries. I still don't get the gist of it in this context. The dialog is as follows.
Leonard: Please, I’m asking you as a friend.
Sheldon: Are you making this a tier-one friendship request?
If he told him "two-tier friendship request", how would the meaning be different?
Best Answer
While the link provided by Damkerng T is interesting I don't think it's particularly likely it has much to do with what Sheldon says. At the very least you don't need that type of information to parse it.
Tier one in general will either mean the highest or the lowest tier. We can infer from the context that Sheldon means it as the highest tier. I.e. as Damkerng T. explains in his second comment what Sheldon is really asking is "Is this really important to you?".
The real point of the sentence is more to reinforce the idea that Sheldon is a very socially inept person for comic effect. Normally people would never phrase the question that way. You wouldn't really even ask "Is this really important to you?", because that is obvious from the preceding conversation. You might say something like "This is really important to you, huh?" or "You'll owe me," where you are already acknowledging the situation and essentially just getting the other person to commit themselves and possibly expressing your slight hesitation.
For comedic effect Sheldon is being portrayed as having to consciously evaluate the level of the friendship and tie it to the request being made.