For a flight booked through the Chase Portal, UA may refuse to rebook directly, or may charge you $50 to take over the ticket from Chase Travel (aka Expedia, last I checked). You'd be expected to go through Chase for this; they're your agent.

The specific language from UA's travel agency website is that they're allowed to "Change to alternate UA flight (same origin and destination)." It does not indicate whether or not a codeshare would be viable; sometimes it's best, whether dealing with a travel agent or a United rep, to feign ignorance of code-sharing. There are some availability limits, though: "same booking class for premium cabin. Contact UA if required class of service is unavailable." So Chase will have to call UA if there are not seats in the same booking class that you purchased.