The design and mass cost of a starship and its life support system are investigated. The mission plan for a multigenerationai interstellar voyage to colonize a new planet is used to describe the starship design, including the crew habitat, accommodations, and life support. Cost is reduced if a small crew travels slowly and lands with minimal equipment. The first human interstellar colonization voyage will probably travel about 10 light years and last hundreds of years. The required travel velocity is achievable by nuclear propulsion using near future technology. To minimize mission mass, the entire starship would not decelerate at the destination. Only small descent vehicles would land on the destination planet. The most mass efficient colonization program would use colonizing crews of only a few dozen. Highly reliable life support can be achieved by providing selected spares and full replacement systems. Two alternate candidate life support approaches are oxygen and water recycling systems with stored dehydrated food or plants grown to provide food, oxygen, and water recycling. The mass costs of such systems using current technology are estimated and compared. Growing food for starship life support requires more mass than providing dehydrated food, even for multigeneration voyages of hundreds of years. The benefits of growing some food may justify the added mass cost. A system growing half the food is competitive with all dehydrated food. Plant growth technology has much more potential for mass reduction than dehydrated food, and currently projected improvements in plant growing technology could make it competitive. The lowest total mission mass is achieved a relatively low interstellar travel velocities. The life support mass saving on shorter voyages is less than the propulsion mass required to increase velocity. Life support is half the total spacecraft mass without propulsion, but propulsion is one and a half times more massive than the spacecraft, so life support is only twenty percent of the spacecraft plus propulsion mass. A single multigenerationai interstellar voyage to colonize a new planet would have cost similar to that of the Apollo program. We can go to the stars!