Of course a chord can have only two notes. The G chord played at the third fret with the F shape, except leaving the G string open, has the notes GDGGDG. There are only two notes although it spans two octaves. It is ambiguous admittedly, having the potential to be major or minor, but it is still a chord. I mean , what else would you call it? Maybe a G power chord?
A diminished chord is the only chord I know which requires four notes to define it. Like B,D,F played together could conceivably be part of a G7 chord, but if you add a G# yjen it is defined as diminished.