A320 Captain experiences center tank fuel pump failure in cruise and opens crossfeed valve in compliance with ECAM. After center tank fuel was depleted a large fuel imbalance between the left and right wing tanks was discovered. Due to aircraft maintenance history and confusion over actual fuel available; the crew elected to divert.

Narrative

During flight [we] had 'CENTER TANK 1 LO PRESS' on ECAM. [We] accomplished ECAM procedure. When center tank [was] no longer feeding; [I] was somewhat surprised to see on fuel page a very large imbalance. The fact that right tank was full suggested to us both engines were being fed from left tank and right tank was not feeding right engine. Even though cross-feed was open per ECAM and we were in process of closing; we concluded left pumps could not completely override right pumps; therefore a feed issue. Because of our uncertainty as to how much if any fuel was available from right tank and our flight path was approaching terrain and not so many good diversion airports; we felt the safest course was to divert to an airport less than 100 miles away. Had the right tank quantity burned down even a small amount; I would have assessed an imbalance vs. a feed problem. The fact the right tank was full along with past aircraft history of fuel problems led us to conclude we had a fuel feed problem; plus the uncertainty of our total fuel quantity; influenced our decision to divert. Normal landing; conferred with Maintenance; and were away in an hour with new airplane.