There are five potential wives for Chrom:
- Olivia
- Sumia
- Avatar
- sully
- Marybelle

So let's start with probably the best choice for chrom's wife, Olivia.

Olivia is good for passing on the Myrimidon and Pegasus Knight classes to Lucina, allowing Lucina access to the powerful skills Galeforce, Lancefaire, Astra, Vantage, and swordfaire. She also raises Lucinas speed and luck even more then they already are. However, the main point of this pairing is getting rightful king on Inigo, which on top of his already top notch skill can make him deadly with skill activated skills.
Take note that this is the most ideal wife for Chrom but also the hardest to pull off, as Chrom doesn't have much time to build support with Olivia because he meets her on the battlefield for the first time. The best thing to do is to keep Chrom away from all females that he can marry, until the map with Olivia. If he has formed support with any of the other women that he can marry he will choose them over Olivia at the end of chapter 10. He will need to Fight a minimum of 9 battles while paired with Olivia to marry Her. You could also use seeds of tufts and dancing, however you would have to dance around 27 times to gain the support. Since this is a hard pairing to pull off, I do not recommend this for your first playthrough.

Now for Sumia.
Sumia passes on nice speed and skill to Lucina as well as giving her the cleric and Pegasus knight classes. Chrom gives Cynthia the archer and cavalier class; Cynthia can make a good sniper with her high skill and speed, so this is a good wife for Chrom as well. The only thing that you might need worry about with this pairing is that Lucina will inherit her mothers frailty.

Avatar is next.
This is a popular combination for first time players, as the Avatar and Chrom are the main Characters in the game, and your first thought is to keep them away from danger. This often puts them paired together. This is the easiest of the pairings to pull off as well, as Chrom and the avatar can begin growing closer in the very first level. As for child inheritance, Lucina gains a wide level of diversity by getting every single class excluding the male and spotpass classes. She gets both the exclusive classes lord and tactician. Morgan gets rightful king from Chrom, a very useful skill as Morgan gets a wide level of diversity as well. This is not the best pairing for Chrom however, as while it is easy to pull off and can make Lucina very powerful, your Avatar is better off marrying a Child Character and having an overly powerful Morgan or marrying a spotpass character and getting an exclusive skill on Morgan.

Sully is up.
Sully is a good first playthrough pairing other than the Avatar. Sully will pass on the Myrimidon class to Lucina giving her all the useful skills of that line. Sully can also pass along the discipline skill to Lucina making training her a little easier. Kjelle gains Aether from Chrom, a good skill for Kjelles type. She also inherits high skill, luck and speed caps from him.

The final one is perhaps the oddest pairing, Chrom plus maribelle.
Lucina wiil get the troubadour class from maribelle, passing along the skills renewal and dual support. She'll also inherit an even higher luck stat. She will also gain the Pegasus knight class, granting the ever popular Galeforce skill. She'll also get maribelles frailty though, so beware. Brady gets rightful king added to his skills, as well as the archer class added to his classpool. Brady gets a nice luck cap from Chrom- although it's not as much as Donnel + maribelle luck cap for Brady, Chrom gives a good boost.

That's it for potential pairings for Chrom. hope this helps! Comment below your favorite Chrom pairing if you want.