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The crystallization of amorphous solid water (ASW) is known to form nano-crystalline ice. The influence of the nanoscale crystallite size on physical properties like the vapor pressure is relevant for processes in which the crystallization of amorphous ices occurs, e.g., in interstellar ices or cold ice cloud formation in planetary atmospheres, but up to now is not well understood. Here, we present laboratory measurements on the saturation vapor pressure over ice crystallized from ASW between 135 and 190 K. Below 160 K, where the crystallization of ASW is known to form nano-crystalline ice, we obtain a saturation vapor pressure that is 100 to 200% higher compared to stable hexagonal ice. This elevated vapor pressure is in striking contrast to the vapor pressure of stacking disordered ice which is expected to be the prevailing ice polymorph at these temperatures with a vapor pressure at most 18% higher than that of hexagonal ice. This apparent discrepancy can be reconciled by assuming that nanoscale crystallites form in the crystallization process of ASW. The high curvature of the nano-crystallites results in a vapor pressure increase that can be described by the Kelvin equation. Our measurements are consistent with the assumption that ASW is the first solid form of ice deposited from the vapor phase at temperatures up to 160 K. Nano-crystalline ice with a mean diameter between 7 and 19 nm forms thereafter by crystallization within the ASW matrix. The estimated crystal sizes are in agreement with reported crystal size measurements and remain stable for hours below 160 K. Thus, this ice polymorph may be regarded as an independent phase for many atmospheric processes below 160K and we parameterize its vapor pressure using a constant Gibbs free energy difference of (982 +/- 182) J mol(-1) relative to hexagonal ice.