Here is your original:
A chance encounter is a great idea.
However, in this case, chances would
be very slim to meet her this way.
Even worse, if I went out of my way to
meet her socially and randomly, chance
that her two roommates would accompany
her are pretty significant
Here it is with minor corrections to clear up the sense in meaning (noted in italics):
A chance encounter is a great idea.
However, in this case, the chance
would be very slim to meet her this
way. Even worse, if I went out of my
way to meet her socially and randomly,
the chance that her two roommates would accompany her would be pretty
significant.
This mainly drags the moods and tenses (and numbers) into agreement and adds articles where I believe they are necessary.
Now please forgive me for taking the liberty, but here's how I would modify the passage if I were your editor:
A chance encounter is a tempting idea.
The chances are slim, however, that I
would meet her this way. And even if I
should contrive to meet her socially
(and "randomly") in this way, there
remains a strong likelihood that her
two roommates would accompany her.
I changed great to tempting because everything that follows suggests the idea is not great; you are merely entertaining the notion. I shortened the next sentence and removed the intensifier very because it adds nothing. The last sense I cast more strongly as a final objection rejecting the premise set up in the first sentence. I also removed most of the uses of subjunctive mood and played it off against the indicative for effect.