What I reason: Calcium chloride is the salt of hydrochloric acid and calcium hydroxide. Calcium hydroxide is usually not considered a strong base, and I believe this is because of it's low solubility. $\ce{HCl}$ is a strong acid, and so the salt should be slightly acidic. Wikipedia states the $\mathrm{p}K_\mathrm{a}$ of $\ce{CaCl2}$ is between 8-9, which is in fact slightly acidic, confirming my theory.
What I've experienced: I've prepared a number of aqueous calcium chloride solutions from distilled water, all of which are purple in the presence of universal indicator and tested with a calibrated $\mathrm{pH}$ probe to be basic. I've tried multiple sources of calcium chloride and each is basic.
TLDR: Theoretically and literature values state that $\ce{CaCl2}$ is acidic, but my empirical evidence shows that it is basic.