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Those notes are the first 5 in the Amaj scale but they are also 5,6,7,R,2 of the Dmaj scale.
To harmonise a scale you build triads on each note of the scale; for each note, you add on top of it every other note until you have a stack of 3, eg
A C# E
B D F#
C# E G#
D F# A
etc.
Play each & listen. Those built on the 1st, 4th, 5th of the scale are major, those built on the 2nd, 3rd, 6th are minor, and the one on the 7th is diminished.
If you want to choose chords one for each note of the riff then the most obvious thing to do is find a triad that has that note in it. You might add interest if you can identify a triad that contains two consecutive notes of the riff (so you don't have to change triad so often), or if you play the same note twice in succession you could find 2 different triads that contain it.
There's loads more to it than that but I reckon you could have fun getting started with this.
Enjoy
Seriously: If you value it, take/fetch it yourself
Google is my saviour. I know it's cheating but still...
http://www.guitar-chords.org.uk/chords-key-a.html
http://www.guitar-chords.org.uk/chords-key-d.html
BUT there's nothing like working it out from first principles for yourself. The information sticks better than learning it by rote.
Seriously: If you value it, take/fetch it yourself
I hear it in E but the trouble is it's a rock riff, so there are chords like D and G that aren't strictly in E major.
Seriously: If you value it, take/fetch it yourself
You could maybe try E E D A over the first couple of bars but there's little choice when he moves to the B and the A.
That riff is so good that IMHO it doesn't need any rhythm guitar over it. Maybe start with a weaker riff that needs enhancing!