I have a 15 watt breaker with my current kitchen lighting and dinnette on it. I would like to add four can lights and jump off one one of the other lights will the breaker support this additional pull? The house is only a year old so the wiring is all up to date.

You should be fine.
Volts X Amps=Watts(120X15=1800).
1800 Watts is what you have for available power.
1800/60=30(You can have 30 60 Watt bulbs).

I would assume you mean 15 AMP breaker. Yes, you have plenty of capacity for 4 lights, particularly if you use R30 CFL floods These use 14 watts and are equal to a 65 watt incandescent flood. Not sure of the lumens but they work great in my cans.

Yes, double check the wire is at least 14 AWG (it should be because it is on a 15 AMP breaker) and you should be set.