The best time to offer live chat support is usually when there is most traffic on a site. In both B2C and B2B businesses this often means in the evening. Web analytics tools (like Google Analytics) can be used to find out exactly what those times are.
Whether the company has fixed service hours on chat or not, they should make sure that the live chat channel is active when most customers are on a site. This also means that the company needs to make sure they have adequate chat agent resources to ensure that visitors are replied immediately, preferably within 10 seconds of time.