Monaco stands a chance at winning the UEFA Champions League competition. This is because Monaco is a potential team and has promising success. With the great players and coach, success is paramount for the team. The other thing is that Monaco has a huge number of supporters and fans who also give the players enough support.
I think they definitely stand a chance of going all the way. They currently lead Group E in the champions League after 4 games played. It doesn't hurt that they won their most recent game either. I'm not a huge soccer fan but I am a fan of other sports. When you lead your division that's usually a good indication that you're a pretty good team.
UEFA Champions League is a serious competition. Monaco is such a tiny country--if it can really even be called a country--that it doesn't stand a reasonable chance at taking home the title. Even if Monaco has been performing well, to believe that they'll take it all the way to winning the championship is unlikely.
AS Monaco FC is not a very good contender for the European title. One thing in soccer is clear; history repeats itself. If a team is not once a winner or at least featured in many previous finals, the title is very far away from it.
Although they appear to be in a formidable form this season, the closest Monaco came to winning the title was the finals in 2004 against FC Porto, for which it lost 3-0.