In a fairly entertaining 120 minutes followed by a penalty kick shootout, Manchester City beat Liverpool in the Capital One Cup final to capture their fourth League Cup trophy and second in three seasons. But more importantly than that, City's win has done Chelsea a favor by granting a Europa League spot to the 6th place finishers in the Premier League as well.
Normally, European spots go to the top 5 teams in the league, plus the winners of the League Cup and the FA Cup. The top 4 qualify for the Champions League (top 3 to groups; 4th place to preliminaries), 5th place enter the Europa League, alongside the two cup winners. However, if said cup winners are already among the Top 5 and thus get to go to Europe already (either the CL or the EL), their Europa League spots go to the next highest placed teams in the league.
Assuming Manchester City do not collapse and finish in the top 4 as they should, the spot normally awarded to the winners of the Capital One Cup instead will go to the 6th place team in the league. If the FA Cup winners also finish in the top 5, then their Europa League spot goes to the 6th place team instead, and the League Cup winners' spot goes to the 7th place team (this matters for which round of the continental competition the team gets to enter). This is exactly what happened last year, when Liverpool (6th) and Southampton (7th) both made it. Before last season, the FA Cup runners-up would get a hand-me-down spot, but that rule had been changed by UEFA.
So, while winning the FA Cup remains Chelsea's best chance* of qualifying for European competition next season (only one top 4 team remains alive in the final eight), we could also accomplish that by finishing 6th. (And possibly even 7th!) Given our recent form, confidence, and the continuing issues of many of the teams above us, perhaps that's not such an outlandish idea. Chelsea are currently just 7 points behind 6th place West Ham United, 8 points behind 5th place Manchester United, and only 4 behind 7th place Southampton with 11 games still to go.
Our last three home matches are against three of the current top four teams. The task at hand will not be easy, but that could make it all the more worthwhile to get it done, however unlikely it might have looked just a few weeks ago.
* Sure, there's also winning the Champions League à la 2012. Anything's possible, I suppose.