Chelsea F.C. vs Arsenal F.C. Watch
Speaking as a Tottenham fan I'd say yes you will, your infrastructure (stadium, training facilities) are too good for you not too and you must have huge amounts of money stashed away, coupled with low debt (like tottenham actually :P) it's pretty probable that at some point you'll be challenging for the title. But I don't think that'll happen until Wenger either steps down or starts to spend on established world class talent.