It depends what you are talking about, and you will need to add a subject to the beginning of your sentence.
It may be a best. could be used if you are talking about something personal like a game score. For example you got a new great bowling score, and think it might be the highest you've ever gotten. In this case, "a best" is used as a short form of "a personal best".
It may be the best. could be used to talk about any situation where there are multiple candidates and one is believed better. For example, when discussing how awesome song #12 is on a CD.
In either of these cases you could substitute "might" for "may". You should keep in mind that "best" is a relative term. Something god awful can still be the best if its competition is worse.