End-to-end automatic speech recognition (ASR) can significantly reduce the burden of developing ASR systems for new languages, by eliminating the need for linguistic information such as pronunciation dictionaries. This also creates an opportunity, which we fully exploit in this paper, to build a monolithic multilingual ASR system with a language-independent neural network architecture. We present a model that can recognize speech in 10 different languages, by directly performing grapheme (character/chunked-character) based speech recognition. The model is based on our hybrid attention/connectionist temporal classification (CTC) architecture which has previously been shown to achieve the state-of-the-art performance in several ASR benchmarks. Here we augment its set of output symbols to include the union of character sets appearing in all the target languages. These include Roman and Cyrillic Alphabets, Arabic numbers, simplified Chinese, and Japanese Kanji/Hiragana/Katakana characters (5,500 characters in all). This allows training of a single multilingual model, whose parameters are shared across all the languages. The model can jointly identify the language and recognize the speech, automatically formatting the recognized text in the appropriate character set. The experiments, which used speech databases composed of Wall Street Journal (English), Corpus of Spontaneous Japanese, HKUST Mandarin CTS, and Voxforge (German, Spanish, French, Italian, Dutch, Portuguese, Russian), demonstrate comparable/superior performance relative to language-dependent end-to-end ASR systems.