Need Help to convert a grammar into Chomsky Form I have to convert the following grammar into Chomsky Form 
$$( \Sigma=\{a,b,c,+\}, \Sigma_Q=\{S,V\},I=S)$$ 
$$S -> S+S|V$$
$$V -> a|b|c$$
My idea is the following:
$$S_0 \rightarrow S$$
$$S \rightarrow ST|V$$
$$T \rightarrow +S$$
$$V \rightarrow A|B|C$$
$$A \rightarrow a$$
$$B \rightarrow b$$
$$C \rightarrow c$$
Could you tell me if this is right?

In a grammar in Chomsky normal form there can only be two types of productions: $A\to BC$ and $A\to a$ where $A,B,C$ are nonterminals (variables, $\Sigma_Q$ in your notation) and $a$ is terminal ($\Sigma$ in your notation).
In particular, "chain productions" which are of the form $A\to B$ are not allowed. You have several of them. In particular, the original productions $V\to a\mid b\mid c$ were OK, while the new $V\to A\mid B\mid C$  isn't. 
You have also introduced a special start symbol $S_0$. In the definition of Chomsky as I know it that s not necessary. Also note your production $T\to +S$ is of "mixed type" (it has both a terminal and a nonterminal) and is illegal.
