Vibrated horizontally, granular material has different convection patterns from those observed for the equivalent vertical vibration. Among the patterns that develop, above the onset of bulk motion, is a four roll convection pattern. Surface sloshing produces two smaller convective rolls above two lower interior rolls. Horizontal vibration creates intermittent gaps between the sidewalls and the heap of material. Avalanches of material into these gaps drives the lower convection rolls. This is a different physical mechanism from that observed in convection driven by vertical vibration. As is well known, convection patterns can drive size segregation, and we illustrate some of these effects.