As a friend.
Throughout the course of the game Chrom meets a lot of people and forms strong bonds with them. While all these relationships can be considered important in one way or another I don't think any can compare to the sort of friendship he shares with Robin. They are two halves of one whole after all. For simplicity's sake I am going to be referring to Robin as male here, just because it's easier to discuss, plus I think there is more to be said about male Robin than female Robin anyway.
"There are better places to take a nap than on the ground you know. Give me your hand."
– Prologue: The Verge of History
Robin makes his appearance in Premonition: Invisible Ties in what appears to be a flashback or vision of events to come where he and Chrom are fighting against a sorcerer named Validar. While the two are successful in defeating him something overcomes Robin and he kills Chrom. We see him again in Prologue: The Verge of History where Chrom, Lissa, and Frederick find him unconsious on the side of the road. When he awakes he appears to have no memory of who he is, but oddly enough seems to know Chrom's name. Although Frederick is wary of him, and thinks he could be a Plegian spy, Chrom is still willing to help him. While they are talking about what to do with Robin Lissa notices a town on fire and they rush to aid in its defense against the bandits razing the town. Robin follows and after helping protect the town it is discovered he has expertise in battle strategy. Because of this Chrom decides to make him an official member of the Shepherds Militia as the new tactician.
Robin's transition into the Shepherds is seamless and to Chrom it feels like he's been a Shepherd for a long time. While most would be skeptical of a man claiming to have no memory of his past, Chrom is trusting of him right away, and nothing anyone says can change that, even when Robin's past is revealed. That he was the son of Validar and was raised for the sole purpose of being a vessel for the fell dragon's return. Even knowing these things Chrom's trust in Robin does not change, not even after Validar is able to gain control of Robin's body and force him to take the Fire Emblem from Chrom. Afraid that Validar could take control of him again Robin begs Chrom to leave him behind and that he is not to be trusted. Chrom disagrees, however, and believes Robin can fight it. Validar never had full control after all, and if he expects Robin to obey blindly, that may be the surprise they need in order to defeat Validar and recover the Fire Emblem.
When Chrom and Robin arrive at the Dragon's Table to confront Validar Robin has Chrom promise him to cut him down if he were to ever lose control. Although Chrom is reluctant to do so, he agrees. There are too many lives at stake. Although they are able to recover the Fire Emblem they are not able to prevent Grima's return as the Grima from the future (who had followed Lucina to the past but lost his powers, taking the form of Robin) claimed the present Grima's powers and returned to his true form. When it comes to defeating the fell dragon they are faced with two options: if Chrom deals the final blow Grima will go back to sleep, however if Robin were to deal the final blow Grima will die. Unfortunately, because the two of them share the same heart Robin will also disappear. Chrom asks that Robin promise he won't kill Grima because he is one of them. Robin can choose whether or not to agree on the promise, but his answer will have no effect on the outcome of the final battle.
Although the game has two different endings, depending on who you let deal the final blow, there is really only one choice for me. I know it's bittersweet, and even a little bit sad, but I always let Robin deal the final blow. One reason is Grima is gone for good, but also because Chrom never stops believing and knows their paths will one day cross again because of their strong bonds, and sure enough they do––in the same field in the same way they first met.