Most theoretical concepts of polymer crystallization have evolved around monolamellar single crystals as model systems. However, such approaches do not account for an important and unique aspect of crystallization of long flexible molecules: the correlated stacking of lamellar crystals. In our experimental work, we focus on the growth kinetics of such stacks of lamellae in thin films of poly(nonadecane methylphosphonate). Interestingly, concurrent with a decrease in lateral lamellar growth, we observed an increase in vertical growth, that is, an increase in the number of stacked crystalline lamellae. Intriguingly, in contrast to lateral lamellar growth, the rate of such vertical growth increased with decreasing degree of undercooling. Moreover, we show the possibility of forming three-dimensional polymer quasi-single crystals. Some of the formed stacks of lamellar crystals were about 100 times thicker than the initial film; that is, they had a thickness of about 20 times the contour length of the polymer and contained about 800 stacked lamellae. We propose that growth kinetics of stacking of lamellae is governed by (i) the probability of forming self-induced nuclei, (ii) the detachment probability of crystalline stems, and (iii) the influx of molten polymers toward the growth front.