The Large Hadron Collision (2010)

Leonard announces that the professor who was to attend a conference in Switzerland and visit CERN's Large Hadron Collider is unable to go, so he has been designated to be the replacement, and he gets to take one guest with him. Sheldon is pleased, assuming that he will be Leonard's guest because they have a roommating agreement that if one roommate gets invited to see the Collider, he would invite the other . In spite of the agreement , Leonard chooses to invite Penny, as the trip would coincide with Valentine's Day, their first together as a couple. Sheldon is upset and tries to pressure both Leonard and Penny to let him go instead, but Leonard insists on bringing Penny and not Sheldon, and Sheldon eventually decides to terminate their friendship. The night before their scheduled trip, Penny falls ill, so Leonard decides to ask Sheldon to accompany him. However, he discovers that Sheldon has also fallen ill, which he suspects he caught when he hugged Penny a day before. As a result, Penny spends Valentine's Day with Sheldon. Leonard, knowing Raj had nothing to do for Valentine's Day, decides to take him to Switzerland instead. They arrive to a hotel room stocked with champagne, roses and chocolates, something that disappoints Leonard as he had forgotten he had ordered it, but which greatly excites Raj, who declares this to be the best Valentine's Day ever.

Title reference: The dispute between Leonard and Sheldon over who gets to be Leonard's guest for the trip to the Large Hadron Collider.