Shell-model calculations have been used to predict the locations of states in 27Si which are analogous to well-studied states in 27Al. From this, we have determined the resonance properties of the known states in 27Si near the 26Al + p threshold. The resulting thermonuclear reaction rate is uncertain by about a factor of ten at low temperatures, but it appears that the 26Al(p, γ) 27Si reaction is too slow to destroy a significant amount of 26Al at these temperatures.