Regarding the first aspect of your question regarding censorship thanks to the first amendment there are no laws forcing censorship on user generated content to the extent that the service you are providing should not be designed for the breach of the law. A prime example of this is the torrent site The Pirate Bay. While the argument could be made all content was user generated content the courts ruled that the webmasters designed the site and marketed it specifically for the purpose of breaching US and international laws. Focusing specifically on chatroom's this would more boil down to the exceptions to the first amendment such as (https://en.wikipedia.org/wiki/United_States_free_speech_exceptions)...
- advocacy of the use of force
- False statements of fact
- Child pornography
- Fighting words and offensive speech
- Speech owned by others
- Commercial speech
- Restrictions based on special capacity of Government
Webmasters can and have been held liable for the user generated content (including chatroom posts) on their sites and the expectations in court are that a webmaster who publishes a service like that adopt a reasonable moderation toolkit and procedure to deal with illegal content in a timely manner (such as reporting users or posts, having them removed from chatroom history, banning repeat offenders, etc). As for the extent of your liability that would depend on the circumstances and would really need to be discussed with a legal professional.
Some specific laws which would be applicable to a chatroom site are...
This is not a definitive list but simply the top 4 which may apply to you.
As for the second part of your question regarding SERP rankings or the site being classified as SPAM the SERP ranking could most certainly be affected depending on the type of posts being made by the users. As for the SPAM aspect not as likely, especially if the rest of your site has genuine useful content and this makes up a simple feature of your site but still possible, becomes more likely if you are intending your whole site to be nothing more that a chatroom, especially if it becomes a room whereby the users involved in the chatroom are not having what would be classified as reasonable chats and instead are simply being obscene (cyber sexual chats) or having flame wars.
For all the above reasons while there is no reason not to setup a chatroom site I would strongly recommend ensuring you have the appropriate tools in place on the site to identify illegal activities and remove them from the chatroom and potentially also ban the offending users to cover your own exhaust vent.