Although rhythm playing sounds good with the fullness of five- or six-string chords, three-string chords are a great way to achieve the fluidity and flexibility that are called for in fills and instrumental breaks. Experimenting and improvising with these small chords is a lot of fun and can keep you occupied for hours on end!

You will eventually want to learn to play this type of chord using any set of three strings, but you will probably find them to be most useful on the first three strings. Two easy shapes to start with are the D major and minor chords:

You can play any major chord with the D shape above or any minor chord with the Dm shape.  Using either fingers or a pick, play only the first three strings of these chords and then experiment with playing them in different positions. You will quickly see how, due to the notes of the chord being all fretted notes, the chords are movable in the same way that barre chords are. For example, if you move the D chord up a fret and play only the first three strings, the chord becomes an E. Move the same chord up again and the chord becomes an E and so on, up the fretboard.

With only two chord shapes, you are able to play the first six chords in the scale harmony. Remember that in the scale harmony all I, IV and V chords are major and all ii, iii and vi chords are minor.
Here are the chords in the key of D:

The root of the chord will always be on the second string in these D chord shapes. In order to play the scale harmony (chords in the key of D), you only need to remember the formula for the major scale (whole step, whole step, half step, whole step, whole step, whole step, half step), and follow that formula with your eye on the second string. Each 1/2 step is one fret on your guitar, so after playing the D chord in the first position (fingers on the 2nd and 3rd frets), you will play the Dm shape at the 3rd fret and again at the 5th fret, followed by the D major shape again at the 7th and 9th frets and the minor shape at the 10th.

When you feel comfortable with those chord shapes,learn four more shapes, which will allow you to play all of the major and minor triads on the first three strings. Here are the chord shapes:

In order to find any major or minor chord (triad), determine on which string you would like to play the root, then locate that note on the string and, placing the appropriate finger on the note, make the chord shape. Practice making all of these chords until you are comfortable with them and can use them in all positions. When you are ready, try using them to play songs you know or make up your own. You will find that you are able to play solo guitar pieces (instrumentals) more easily with these smaller chords and you can even play chord melody!