There is a lot of online brokers that self-directed investors can use for buying and selling blue chip stocks. Following list presents few good examples of such brokers.

E*TRADE

E-Trade Financial Corporation is an online discount stock brokerage company. Securities to trade: stocks, bonds, options, mutual funds, and exchange-traded funds. Website: https://us.etrade.com/home, https://www.optionshouse.com/ Finra BrokerCheck for E*TRADE: https://brokercheck.finra.org/…ummary/29106

TD Ameritrade

TD Ameritrade is an online broker. Securities to trade: stocks, futures, ETFs, option trades, mutual funds. Website: https://www.tdameritrade.com/home.page Finra BrokerCheck for TD Ameritrade: https://brokercheck.finra.org/…summary/7870

Scottrade

Scottrade is a discount brokerage firm. Its CEO has been Rodger O. Riney since 1980. Website: https://www.scottrade.com/ Finra BrokerCheck for Scottrade: https://brokercheck.finra.org/…summary/8206

Fidelity Investments

Fidelity Investments is a financial services corporation and discount brokerage. Securities to trade: mutual funds, stocks, etc. Website: https://www.fidelity.com/ Finra BrokerCheck for Fidelity: https://brokercheck.finra.org/…summary/7784

Charles Schwab

The Charles Schwab Corporation is a brokerage and banking company. Schwab serves 9.3 million client brokerage accounts, with $2.40 trillion in assets (as of June 2014). Securities to trade: stocks, ETFs etc. Website: https://www.schwab.com/

Vanguard

The Vanguard Group is an investment management company Securities to trade: mutual funds, exchange-traded funds (ETFs), stocks, CDs, bonds. Website: https://investor.vanguard.com/home/

Morgan Stanley

Morgan Stanley is a financial services corporation and online brokerage. Website: https://www.morganstanley.com/

TradeKing

TradeKing is a discount online brokerage firm. Securities to trade: stocks, options, bonds, ETFs, forex, and mutual funds. Website: https://www.tradeking.com/ Finra BrokerCheck for TradeKing: https://brokercheck.finra.org/…mmary/136131

FXCM

Forex Capital Markets (FXCM) is an online broker. Securities to trade: margin forex trading, contract for difference (CFDs) on major indices and commodities. Website: https://www.fxcm.com/

For comparison of online brokerages please see the list on Wikipedia. This comparison includes Capital One Investing, Charles Schwab, E-Trade, Fidelity, Firstrade, Interactive Brokers, Lightspeed, Web Trader, Merrill Edge, OptionsXpress, Robinhood Markets, Scottrade, SogoTrade, TD Ameritrade, thinkorswim, TradeKing, TradeStation, USAA, Vanguard, WellsTrade and Zions Direct.