Any particular recording you were referring to?
The line itself is just going up chromatically from a Em chord to an Am chord (if you're in E minor, that is), passing Fm, F#m, etc., along the way. The main part starts on the 5th (B) and walks up to E, but you could start from any chord tone in either hand and it would probably sound good too. Starting on E and moving up chromatically to A in the bass would be particularly sensible, since the bass is going to want to wind up on A for the Am chord at the end anyway.
To get the full sound of those ascending minor chords, you could harmonize the RH part a third lower. That is, play G and B in the RH and move both up chromatically to C and E, while the bass goes E to A.
To execute this or any other chromatic scale in the left hand, take advantage of the fact that any regular bass note is a half-step higher than the counterbass one "floor" up*. So you could go
E F
F# G
G# A.
Although, once I hear the example you're talking about, it might be that they're doing something totally different, in which case nevermind.
* I call this a "shark fin" with my students to help them remember, because A) the two buttons are diagonal, like a little shark fin, and B) you can play the "Jaws" theme with it.
