1. We need to count chiral alcohols having molecular formula $C_4H_{10}O$.

2. First, list all alcohol isomers of $C_4H_{10}O$ (exclude ethers, since the question asks only alcohols).

For $C_4H_{10}O$, the alcohol isomers are:

• Butan-1-ol: $CH_3CH_2CH_2CH_2OH$
• Butan-2-ol: $CH_3CH(OH)CH_2CH_3$
• 2-Methylpropan-1-ol: $(CH_3)_2CHCH_2OH$
• 2-Methylpropan-2-ol: $(CH_3)_3COH$

3. Now check chirality of each alcohol.

(i) Butan-1-ol

Structure: $CH_3CH_2CH_2CH_2OH$

No carbon has four different substituents. So, it is achiral.

(ii) Butan-2-ol

Structure: $CH_3CH(OH)CH_2CH_3$

The second carbon is attached to:

• $OH$
• $H$
• $CH_3$
• $CH_2CH_3$

These are four different groups, so this carbon is a chiral center. Hence, butan-2-ol is chiral.

(iii) 2-Methylpropan-1-ol

Structure: $(CH_3)_2CHCH_2OH$

The central carbon is attached to:

• $CH_3$
• $CH_3$
• $CH_2OH$
• $H$

Since two groups are identical ($CH_3$ and $CH_3$), it is not chiral.

(iv) 2-Methylpropan-2-ol

Structure: $(CH_3)_3COH$

The central carbon is attached to three identical $CH_3$ groups, so it is achiral.

4. Therefore, only one alcohol structure is chiral:

• Butan-2-ol

5. Note: Butan-2-ol exists as two enantiomers $(R)$ and $(S)$, but the question asks for the number of chiral alcohol(s), i.e. the number of chiral compounds/structures, not stereoisomers counted separately unless explicitly stated.

So the required number is: $1$