Shares in some of the biggest shale companies soared on hopes that Chevron Corp.’s $33 billion deal to acquire Anadarko Petroleum Corp. could start a wave of consolidation in the U.S. oil patch.

Pioneer Natural Resources Co., Concho Resources Inc. and Parsley Energy Inc. shares each surged more than 8% Friday, as investors speculated that bigger players’ long-expected gobbling up of smaller ones could finally be at hand. Meanwhile, a broader index of U.S. oil-and-gas companies was up about 3%, compared with an increase of...