It depends on the style and how important the melody note is. (PS: There's another chord option, the iii7:
E G B D, which will basically always go to an A chord.)
In "classical" harmony, if this is an important melody note that's held for a full beat or so, it will usually be a part of the underlying chord.
But not every melody pitch has to be a part of the chord; there are several kinds of non-chord tones (often abbreviated "NCTs", and also called "non-harmonic tones") to introduce some dissonance and tension into the relationship between harmony and melody. Often these non-chord tones are just subsidiary, 'less important' pitches within the melody.
Take, for instance, this popular children's tune:
In the first two measures, you'll see that the A and F aren't a part of the C chord. But they're also on weak parts of the measure; the pitches on the strong beats (1 and 3) are G, G, E, and G, all parts of the C major triad. The same is true in m. 3: the pitch on the weak beat 2, E, is not part of the chord (the F makes it a G7 chord). You can test this out in m. 4, as well. These non-chord tones aren't always on the weak beat, but it's a good starting spot to learn about the concept.
As Ben suggests in the comments, it also depends on how you define chords. If you're just dealing with triads, a triad will only have three pitches in it. But if you're looking at thirteenth chords, suddenly you have seven different chord tones!
And when we get into popular/rock music, there is this great concept of the "melodic-harmonic divorce" (search for it online) where the melodies are sometimes directly at odds with the underlying harmonies.