NEW YORK ( TheStreet) -- Citigroup ( C) shareholders' "stinging rebuke" of CEO Vikram Pandit's $15 million pay this week is a skirmish in a potentially precedent-setting war that some of the biggest institutional investors will be waging at annual meetings.New York City and California state pension funds, among others, are expecting support for proposals that allow shareholders with a 3% stake (held for at least three years) to nominate board directors. Large shareholders have been waiting for this chance for years. Boards are famous for indulging management and playing into CEOs' interests. A lawsuit brought by the Chamber of Commerce and others that was resolved in late 2011 -- which challenged the Securities and Exchange Commission over its attempt to implement a similar proposal on a market-wide basis -- has opened the door to challenges targeting individual companies. Institutions have zeroed in on two companies in the energy sector: Chesapeake Energy ( CHK) and Nabors Industries ( NBR). And for good reason. Pension funds including CalSTRS and the New York City pension funds represented by the city's Office of the Comptroller, have targeted Chesapeake and Nabors because the proposals are likely to have the greatest chance of being approved by shareholders due to long-standing complaints about CEOs running personal fiefdoms with rubber-stamp directors. In the latest sign of shareholder frustration with Chesapeake, Reuters reported this week on more than $1 billion in personal loans that the company's CEO, Aubrey McClendon, had tied to his stakes in Chesapeake wells, a revelation that led to one of the most massive days of selling in Chesapeake share history. Argus Research analyst Phil Weiss concluded: "The best thing for investors would be to replace the board and/or the CEO." Michael Garland, head of corporate governance for the New York City comptroller's office, said in an email to TheStreet: "This is fundamentally a failure of Chesapeake's board, which has repeatedly shown itself to be incapable of providing independent oversight of a risk-addicted CEO. What is most troubling in this case is that the board was reportedly aware of the loans yet failed to either review or approve them. Chesapeake's long-term shareowners need directors who will protect our interests, not those of a self-interested CEO." Chesapeake Energy shares are trading at a four-year low, though at least in part due to a decade-low price in natural gas.