How to make my enemy jump over obstacles?

It's way more complicated: you must create an AI (Artificial Intelligence) script to control your enemy. It could use Rigidbody.SweepTest with a short distance (1, for instance) to see if the enemy will collide with something ahead, and make it jump if there's an obstacle. An alternative could be to use a trigger childed to your your enemy and positioned a little ahead, so when something hit it you could make the enemy jump.

EDITED: Well, this is basically your original script with some optimization and the code to jump automatically included - it will jump when colliding to some lateral object (it collides with the ground all the time, so collisions with normals above 30 degrees (sin = 0.5) are ignored. I added also a "jetpack" feature to pass over the abyss - when there is no ground down to 20m below it, the jetpack is turned on until it finds ground. Your enemy must be a CharacterController: if it's not, add it using the menu option Component/Physics/Character Controller.

using UnityEngine; using System.Collections;

public class Enemy : MonoBehaviour {

 public float speed = 4f;
 public float jetPackSpeed = 0.3f;
 public float jumpSpeed = 8f;
 public float gravity = 10;

 private Transform _Player; 
 private CharacterController character;
 private Transform tr;
 private float vSpeed = 0f;
 private bool jump = false;
 
 void Start ()
 {
     _Player = GameObject.FindGameObjectWithTag("Player").transform;
     character = GetComponent<CharacterController>();
     tr = transform;
 }

 void Update ()
 {    // find the vector enemy -> player
     Vector3 chaseDir = _Player.position - tr.position;
     chaseDir.y = 0; // let only the horizontal direction
     float distance = chaseDir.magnitude;  // get the distance
     if (distance <= 2)
         Debug.Log("Attacking Player");
     else
     {    // find the player direction
         Quaternion rot = Quaternion.LookRotation(chaseDir);
         // rotate to his direction
         tr.rotation = Quaternion.Slerp(tr.rotation, rot, Time.deltaTime * 4);
         if (character.isGrounded){ // if is grounded...
             vSpeed = 0;  // vertical speed  is zero
             if (jump){    // if should jump...
                 vSpeed = jumpSpeed; // aplly jump speed
                 jump = false; // only jump once!
             }
         } 
         else // but if lost ground, check if it's an abyss
         if (!Physics.Raycast(tr.position, -tr.up, 20f)){ // if no ground below
             vSpeed = jetPackSpeed;  // use jetpack
         }
         vSpeed -= gravity * Time.deltaTime; // apply gravity
         // calculate horizontal velocity vector
         chaseDir = chaseDir.normalized * speed;
         chaseDir.y += vSpeed; // include vertical speed
         // and move the enemy
         character.Move(chaseDir * Time.deltaTime);
     }
 }
 
 // if collided with some wall or block, jump
 void OnControllerColliderHit(ControllerColliderHit hit){
     // only check lateral collisions
     if (Mathf.Abs(hit.normal.y) < 0.5){
         jump = true; // jump if collided laterally
     }
 }

}