The thing you left out was this, and just to make it a little easier to understand we'll do it from the G note in the 3rd fret, on the 6th string. You're right about the 4 frets, start there and go up to the A# note in the 6th fret.

When you go to the 5th string, you start in the 2nd fret. If you start in the 3rd fret, like you did on the 6th string you'll miss the B note in the 2nd fret. Go up to the D note in the 5th fret on the 5th string.

When you go to the 4th string, you start in the 1st fret. If you start in the 2nd fret, like you did on the 5th string you'll miss the D# note in the 1st fret. Go up the the F# note in the 4th fret on the 4th string.

Since that's an F# note, the next one coming up is a G. So you play the 3rd string open, and go up to the A# note in the 3rd fret.

Play the B string open, and go up to the D# note in the 4th fret.

Play the 1st string open, and go up to the G note in the 3rd fret.

This will vary as you go up the neck, but most of the time when you move to another string, you will start one fret before where you started on the previous string. Chromatic is playing every note, by moving up in half steps. If you know your musical alphabet, then it's fairly easy to figure these out.

Mick J was right about the fingering, and this is a great way to learn notes on the fret board, and a good finger exercise too. You can also practice like Mick J said, but it won't be a chromatic scale, just a good workout for the fingers.

Mick J was also right about the A major scale, and the same fingering is used for the other major scales as you go up the neck. Going down the F# major scale, which starts in the 2nd fret on the 6th string, would be the last time you could play this scale pattern. From here all the way up the neck, to the C major scale that starts in the 20th fret. You can only go that high up, if your guitar has 22 frets though.