Really any DAW is capable of composing 'chiptunes' as they are most often composed of the simplest wave forms. It is up to you, would you prefer a tracker or a sequencer? do you want a basic program or one with built in effects (such as filters, eq, delay etc.)?
The DAW is a tool for you to use to compose with, if you don't know how to compose already or have a decent idea at least, using the programs will be of little use; sure you can screw around in the programs and maybe even come up with something half decent but really you need to learn basic theory and if possible learning some piano would help you immensly.
Now if you already have a good idea on how to compose or play an instrument like the piano and can come up with some decent tunes here are some programs I have come across in my endeavours:
Trackers(there are a lot out there so I will only mention some I have some experience with):
MilkyTracker - Free. Very basic tracker in terms of effects* and interface, but decently powerful and has all the features you really would need for chip tune tracking. Focuses on creating your own samples and you could say on chiptune music but I believe you can import other samples also. Also has a decent user base and a few tutorials and examples on the net.
Renoise - Not free (website down at time of this post so I am unaware of exactly how much it costs, but it is somewhat negligible). Feature rich DAW with VST support and effects, can be used for chiptunes but also much more. I really like this program but I am prefer to use the free options myself. Big(ish) community. Nice interface and controls.
SunVox - Free. I recently discovered this and I am loving it. Features its own built in effects and synthesizer, no VST support though. Nice modular approach to the interface and the effects and synth's allows for a lot of possibilities, also has a piano roll and is able to stack patterns which are nice features that work well with the tracker interface. Not a very big userbase though the developer has an active Youtube channel and there are some resources out there(look for SolarLune on these forums and there should be some tutorials that he created linked in his signature).
Sequencer:Fl Studio - You obviously know of and perhaps have used FL studio. I have played around in it from back when it was called frooty loops, and it is a great program for beginners. Feature rich with many built in effects, easy to use and learn interface(although it is ugly in my opinion). Probably the most beginner friendly and has a massive community with a lot of resources out there for it. Certainly capable of making chiptunes but is more slanted to creating trance(and other likewise electronic music). The main downfall is the price for myself.
Reaper - Very capable program easily on par with the big DAW's and for a fraction of the cost. Fully featured program with built in effects. Great for recording with and for producing all kinds of music, but slanted very much towards more professional music composition, though still very capable of doing chiptunes. Great interface.. once you learn it, probably not the most beginner friendly program but once you get better and if you want to branch out to more with music, keep this in mind.
Don't let this be a discouragement to yourself in any way, that is not my purpose, but what I recommend is (if you haven't already) gaining some music knowledge (Chords, scales, intervals etc) while you learn any of these programs, it will help you a heap and you will have an understanding of how music works. Learning to play and compose music takes a long time and there is a lot to learn, I myself am also learning every day and have much to learn but I recommend you give it a go as it is highly rewarding and enjoyable(although there are the odd frustrations).
*effects in the sense of compressor, delay, reverb, eq etc
Also this is entirely based off of my opinion and experience, every point may not be 100% accurate. 
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