If not working as hard was all it took for society to reject someone, there wouldn't be much society left. Or maybe it was at some point, leading the vast majority of the human species that didn't cut it to go "Fuck those guys" and wander off to do their own thing, only with hookers and blow, and are now the only things still alive.
... beyond that, it'd depend on how the chip works. S'currently a straight fact that some antidepressants and whatnot (the closest equivalent we have to happiness chips, unless you want to start comparing them to recreational drugs) actually confer a competitive advantage when it comes to hard work -- it's one of the reasons there's an existent problem vis a vis drug abuse of those particular substances. People with normal endorphin and whatnot balances use 'em largely just so they can work harder.
Really, though... it's questionable if the latter actually would be inclined to work harder. Natural happiness is significantly more inconsistent than a technologically maintained one would be (conceptually, anyway), which means that the motivation of those dealing with it are going to trough and peak sporadically and commonly, regularly disrupting their capability and relative interest in doing work. Their highs may (may) be higher, but they would also have lows at all and those highs wouldn't have a frequency of "always". Your chiphead wouldn't have that problem, and would have one less point of inconsistency in regards to their working patterns. I can tell you right now which of those two almost any business (or any other sort of organization, or most interpersonal considerations, or...) in existence would value more and it ain't the baseline critter :V
Generally, unemployed individuals are less fit for child-rearing, and while love might not be superficial enough to consider only finances or productivity, it is still a cooperation of sort, so someone who does not contribute to society and people around would, you know, not contribute to their fiance either. That's more or less a toxic relationship.
Relationships generally lead to reproduction, or in the case of biologically-incompatible mates, adoption, and in the case of childless mates, to mutual aid in survival which has a ripple effect on society's survival as a whole.
So someone who doesn't "work" would more or less be filtered out from the gene pool, and their ideas filtered out from the collective superego due to them being, y'know, useless.
Addendum: And maybe I shoudl change my opinion from the importance of earned happiness to more on the importance of a system of work-reward. We don't need to be happy, per se, we just need a reason to contribute to society and/or ourselves.
And it's probably a big point in philosophy whether or not people even need to be selfless. This will probably be even a bigger issue when we get robot slaves. My opinion is that it doesn't really matter whether or not it is ethical or not to be selfish. If humans were completely selfish and doesn't contribute whatsoever in a human-robot society, then humans will go extinct. Not even because the robots will rebel, but because humans will just die off because we can't be arsed to reproduce.