We analyze the competitive capacity investment timing decisions of both established firms and start-ups entering new markets, which have a high degree of demand uncertainty. Firms may invest in capacity early (when uncertainty is high) or late (when uncertainty has been resolved), possibly at different costs. Established firms choose an investment timing and capacity level to maximize expected profits, whereas start-ups make those choices to maximize the probability of survival. When a start-up competes against an established firm, we find that when demand uncertainty is high and costs do not decline too severely over time, the start-up takes a leadership role and invests first in capacity, whereas the established firm follows; by contrast, when two established firms compete in an otherwise identical game, both firms invest late. We conclude that the threat of firm failure significantly impacts the dynamics of competition involving start-ups.