I take a darker view of the slogan. It seems to me that it is urging potential lottery ticket buyers to accept that buying a ticket in hopes of winning the lottery is the only "chance to dream" that they have. It's hard to think of creepier and more cynical sales hook than that—particularly a sales hook associated with a less-likely-than-being-struck-by-lightning chance of hitting it big.
The psychology of sales pitches for lotteries is fascinating. As Jim notes in a comment above, a longstanding pitch for the Maryland Lottery (I believe) was "Ya gotta play to win!" which frames the purchase as a form of play involving a simple, exciting game. Likewise, other ad campaigns for lotteries, casino gambling, etc., focus on inviting prospective gamblers to "join the fun."
When I lived in New York City—a town whose denizens pride themselves on their street-smart, I'm-no-patsy outlook—a series of radio ads for the lottery adopted the tactic of asking everyday people why they "play the lottery." One memorable answer came from a native New Yorker who said "So I risk a buck—figure I might get lucky!" Just the right tone of not expecting to win (the way a chump would) but emphasizing that the stakes were so low ("a buck") that gambling actually made a kind of tough-guy sense. I waited in vain for one of the respondents to say, "Are you kiddin'? I really think I'm gonna win!"