The requirement to carry a chart is in NCO.GEN.135(a)(10):
current and suitable aeronautical charts for the route of the proposed flight and all routes along which it is reasonable to expect that the flight may be diverted;
Electronic versions are explicitly allowed in the Guidance Material in the AMC to Part-NCO:
GM1 NCO.GEN.135 Documents, manuals and information to be carried
GENERAL
. . .
(b) The documents, manuals and information may be available in a form other than on printed paper. An electronic storage medium is acceptable if accessibility, usability and reliability can be assured.